Been doing a lot of reading on this. My answer is...YES.
The Kid was a Wanted Man at the time. He had a $500 bounty on his head.
Based on my reading, how I think it went down:
1) Sheriff Pat Garret was hunting down The Kid. In a dark-room, Garret thought he heard The Kid's voice. Garret shot him, man down, he's dead. Uh-oh...it's NOT the Kid.
...Garret is now on the hook for murder of an innocent man. Garret knew the routine. Pay off some heads to sign off on confirmation of the body. That's The Kid, right? Here's ten bucks. Get this body underground ASAP.
...The Kid gets wind of this situation. Garret claiming that the Kid is dead. The Kid heads down to Mexico, he's no dummy. Stays underground for years.