EXHIBIT 32.1

Certification of Chief Executive Officer and Chief Financial Officer

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

J. Bruce Whittaker, President and Chief Executive Officer, and Michelle M. Plummer, Chief Financial Officer, of Greene County Bancorp, Inc. (the “Company”) each certify in his or her capacity as an officer of the Company that he or she has reviewed the Annual Report of the Company on Form 10-KSB for the year ended June 30, 2004 and that to the best of his or her knowledge:

1.    the report fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934; and

2.    the information contained in the report fairly presents, in all material respects, the financial condition and results of operations of the Company.

The purpose of this statement is solely to comply with Title 18, Chapter 63, Section 1350 of the United States Code, as amended by Section 906 of the Sarbanes-Oxley Act of 2002.

September  27, 2004   _/s/ J. Bruce Whittaker__________________

Date   J. Bruce Whittaker

                                                                                                             President and Chief Executive Officer 

September  27, 2004   _/s/ Michelle M. Plummer________________

Date             Michelle M. Plummer

                                                                                                              Chief Financial Officer