I searched the Civil War Research Database for the 37th which is rather sketchy.
The unit fought at Perryville, KY on Oct 8, 1862 in which four men were mortally wounded with death dates of 10/16, 19, 21 & 11/6.
A Capt. Dantzler is listed as killed 10/3/62 at the Battle of Cornith.
There is no mention of where they died [Dantzler excepted] or were buried. Your best bet is obtaining his service records, however, there is no guarantee you will find this information there.