Richard,
I've reviewed some of the abbreviated service record information for Union soldiers from the state of Ohio. There are seven (7) Samuel Bairds listed. Only one matches up based on age:
Name: Samuel Baird
Enlistment Date: 2 May 1864
Service Record:
Enlisted as a Captain on 2 May 1864 at the age of 36.
Commission in Company H, 150th Infantry Regiment Ohio on 2 May 1864.
Mustered Out Company H, 150th Infantry Regiment Ohio on 23 Aug 1864 at Cleveland, OH.
I've done a pension search and do not find a pension application for this man or his wife/widow in the pension indexes.
You can obtain this man's Compiled Military Service Record through the link below, which should have additional information.
Jim Martin