Can State or Local Police Arrest/Charge You For Federal Firearm Possession If Not Prohibited By State

By Tx & Ks law a felon can legally possess a firearm under certain circumstances. Say that this felon was previously convicted of federal charges but legal to own a firearm according to state law. Say he is pulled over in Ks by local/state police and a gun is found. Say the only crime he is committing is federal felon in possession of firearm. Apply a similar situation to a felon in Tx but this time his house instead of his car. Say a warrant is served and nothing besides a shotgun is found. In both situations can state/local police arrest the felon? If so how common is it and what do local/state police do with him after his arrest? If not can they report our felon to the feds? If so does this ever happen and can the feds prosecute our felon strictly on a state/local officers testimony?