An off-duty police officer yesterday shot and wounded a man who was trying to steal his motorcycle from a Brooklyn alley, officials said.

According to sources, Troy Luis was sleeping in his first-floor Brownsville apartment shortly before 2:30 a.m. when he was awakened by the sound of his Suzuki GSX in the alley below his window, where two men were trying to make off with the bike.

Luis quickly got dressed, grabbed his gun and shield and told his wife to call 911.

Luis identified himself as a police officer and confronted one of the men, who turned and fled along Tapscott Street, cops said.

Police said what happened next is still under investigation. Sources said the suspect said, “F- -k that police shit” before four shots rang out.

Lucious Welcome, 30, was struck once in the neck before fleeing over a razor-wire fence, police said. Responding officers found him hiding behind a three-foot wall.

No weapon was recovered.

Welcome was taken to Brookdale Hospital, where he was in stable condition. He also suffered lacerations to his arms and legs from the fence’s razor wife.

The second suspect got away.