You may procure his service records files which includes his reenlistment bounty payment statement with his signature at:
http://history-sites.com/research/index.html

Robert H. Barrett

Residence was not listed;
Enlisted on 6/1/1862 at Tazewell, VA as a Private.
On 6/1/1862 he mustered into "H" Co. VA 29th Infantry
(date and method of discharge not given)
He was listed as:
* Furloughed 11/30/1862 (place not stated) (Home, sick)
* Returned 3/5/1863 (place not stated)
* On rolls 4/15/1863 (place not stated)
Other Information:
born in Virginia
(Born 1830. Living in Tazewell, VA in 1898)