THere are 2 WIlliam J Crawfords on the Civil war database.

1. 10th Ky cav. Union. THis is not your guy because that unit seems to be a northern and Northeatern Kentucky unit.
2. William J Crawford of the 23rd Kentucky Inf. It was formed in Lexington. We need help with info, but I doubt this is your guy either.

THere is a William Crawford in the 7th Ky. Inf CSA/ THis is a Western Kentucky unit so it might be your guy.
THere is also a William Craford in the 17th Ky. Inf. UNionist. It was formed in Ohio CO. so it may be your guy.
I wish I could help more, but I tried. George Martin or ALan PItts to the rescue LOL!!
Take care!!
JAck