<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>114 - Disclosure - Customer Deposits</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>P01_01_2013To06_30_2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000844985</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>2</Level><ElementName>us-gaap_DepositLiabilitiesDisclosuresTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="P01_01_2013To06_30_2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>              &lt;table border="0" style="clear:both;width:100%; table-layout:fixed;"&gt;  &lt;tr&gt;  &lt;td&gt;&lt;/td&gt;  &lt;/tr&gt;  &lt;/table&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;MARGIN: 0pt 0px; FONT: 10pt Times New Roman, Times, Serif "&gt;  &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;MARGIN: 0in 0in 0pt; FONT-SIZE: 10pt"&gt;  &lt;table style="clear:both;WIDTH: 100%; BORDER-COLLAPSE: collapse"  border="0" cellspacing="0" cellpadding="0" width="100%"&gt;  &lt;tr&gt;  &lt;td style="BORDER-BOTTOM: #f0f0f0; BORDER-LEFT: #f0f0f0; PADDING-BOTTOM: 0in; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0in; WIDTH: 7%; PADDING-RIGHT: 0in; BORDER-TOP: #f0f0f0; BORDER-RIGHT: #f0f0f0; PADDING-TOP: 0in"   valign="top" width="7%"&gt;  &lt;div style="clear:both;MARGIN: 0in 0in 0pt"&gt;&lt;b&gt;&lt;font style="COLOR: black; FONT-SIZE: 10pt"&gt;10.&lt;/font&gt;&lt;/b&gt;&lt;font style="FONT-SIZE: 10pt"&gt;&lt;/font&gt;&lt;/div&gt;  &lt;/td&gt;  &lt;td style="BORDER-BOTTOM: #f0f0f0; BORDER-LEFT: #f0f0f0; PADDING-BOTTOM: 0in; BACKGROUND-COLOR: transparent; PADDING-LEFT: 0in; WIDTH: 93%; PADDING-RIGHT: 0in; BORDER-TOP: #f0f0f0; BORDER-RIGHT: #f0f0f0; PADDING-TOP: 0in"   valign="top" width="93%"&gt;  &lt;div style="clear:both;MARGIN: 0in 0in 0pt"&gt;&lt;b&gt;&lt;font style="COLOR: black; FONT-SIZE: 10pt"&gt;Customer Deposits&lt;/font&gt;&lt;/b&gt;&lt;font  style="FONT-SIZE: 10pt"&gt;&lt;/font&gt;&lt;/div&gt;  &lt;/td&gt;  &lt;/tr&gt;  &lt;/table&gt;  &lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;MARGIN: 0in 0in 0pt 0.55in"   align="justify"&gt;&lt;font style="FONT-SIZE: 10pt"&gt;&amp;#160;&lt;/font&gt;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;MARGIN: 0in 0in 0pt 0.5in"   align="justify"&gt;&lt;font style="FONT-SIZE: 10pt"&gt;Customer deposits  represent amounts paid to the Company by customers for devices in  advance of manufacturing completion and/or shipment of the device  to the customer.&amp;#160;&amp;#160;Deposit amounts may vary depending on  the contract.&amp;#160;&amp;#160;Included in customer deposits at June 30,  2013 and December 31, 2012 were deposits of approximately $669,000  from a customer that had placed an order in 2007 for five Nuclear  Pharm-Assist&amp;#153; systems.&amp;#160;&amp;#160;As of the date of this  report, there can be no assurance that this customer will fulfill  its order for these devices.&lt;/font&gt;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;MARGIN: 0in 0in 0pt"&gt;  &lt;font style="FONT-SIZE: 10pt"&gt;&amp;#160;&lt;/font&gt;&lt;/div&gt;    &lt;div style="clear:both; FONT-FAMILY:Times New Roman;FONT-SIZE: 10pt;TEXT-INDENT: 0in; MARGIN: 0in 0in 0in 0.5in"   align="justify"&gt;&lt;font style="COLOR: black; FONT-SIZE: 10pt"&gt;Also,  included in customer deposits at&lt;/font&gt; &lt;font style="FONT-SIZE: 10pt"&gt;June 30, 2013 &lt;font style="COLOR: black"&gt;and  December 31, 2012 were current deposits&lt;/font&gt;&lt;/font&gt; &lt;font style="FONT-SIZE: 10pt"&gt;&lt;font style="COLOR: black"&gt;of approximately  $35,000 and $77,000, respectively.&lt;/font&gt;&lt;/font&gt;&lt;/div&gt;  &lt;/div&gt;        </NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for deposit liabilities including data and tables. It may include a description of the entity's deposit liabilities, the aggregate amount of time deposits (including certificates of deposit) in denominations of $100,000 or more at the balance sheet date; the aggregate amount of any demand deposits that have been reclassified as loan balances, such as overdrafts, at the balance sheet date; deposits that are received on terms other than those in the normal course of business, the amount of accrued interest on deposit liabilities; securities, mortgage loans or other financial instruments that serve as collateral for deposits; for time deposits having a remaining term of more than one year, the aggregate amount of maturities for each of the five years following the balance sheet date; and the weighted average interest rate for all deposit liabilities held by the entity.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 942

 -SubTopic 405

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6479006&amp;loc=d3e64164-112818



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 942

 -SubTopic 210

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.9-03.12)

 -URI http://asc.fasb.org/extlink&amp;oid=6876686&amp;loc=d3e534808-122878



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