Dale,
I believe Richard May's service records will reveal he died at Port Hudson, LA.
May Richard Pvt., Co. F, 39th Miss. Name appears in Port Hudson Post Hospital Ledger; 2-20-1863; hernia; sent to Clinton Hospital 2-22-1863. [Died at Port Hudson 7-1-1863.].
Source:
http://pth.thehardyparty.com/
He is listed as buried at this site.
Port Hudson Battlefield -Hwy. 61, 15 miles north of Baton Rouge, LA; no official cemetery and battlefield encompasses portions of East Baton Rouge Parish and East Feliciana.
Source:
http://www.lascv.com/burial.htm
Hope this helps,
Mitchell