Pension and Other Postretirement Benefits - Net Periodic Pension Costs (Details) - USD ($) $ in Thousands	12 Months Ended
	Mar. 31, 2020	Mar. 31, 2019	Mar. 31, 2018
Defined Benefit Plan Disclosure [Line Items]
Service cost	$ 461	$ 456
Interest cost	3,982	4,555
U.S. Plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	250	250
Interest cost	2,562	3,028
Non-U.S. Plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	211	206
Interest cost	1,420	1,527
Pension Plan | U.S. Plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	250	250	$ 280
Interest cost	2,562	3,028	2,818
Expected return on plan assets	(1,990)	(2,265)	(2,382)
Amortization of actuarial losses	964	934	1,102
Amortization of prior service cost	40	40	40
Special termination benefits	0	0	0
Settlement charges	812	1,206	0
Net periodic pension cost (benefit)	2,638	3,193	1,858
Pension Plan | Non-U.S. Plans
Defined Benefit Plan Disclosure [Line Items]
Service cost	211	206	183
Interest cost	1,420	1,527	1,496
Expected return on plan assets	(2,415)	(2,667)	(2,817)
Amortization of actuarial losses	901	741	952
Amortization of prior service cost	2	2	3
Special termination benefits	0	28	9
Settlement charges	0	(75)	0
Net periodic pension cost (benefit)	$ 119	$ (238)	$ (174)