Two off-duty corrections officers were arrested in separate incidents in The Bronx, police said yesterday.

Capt. Darrel Williams, 48, got into a vicious fight in Norwood and assaulted a man with a wooden plank outside 227 E. 204th St., near the Grand Concourse, about 4:55 p.m. Friday, cops said.

Williams, whose relationship to the victim wasn’t immediately clear, was charged with assault.

And Officer Preston Menefee, 46, allegedly tried to pick up a prostitute, who sources said was actually an undercover cop.

Menefee was cruising around Hunts Point when he stopped along Burnett Place about 8:40 p.m. Friday and made the illicit offer, police sources said.

He was charged with patronizing a prostitute.

Sources said the Department of Correction would investigate the off-duty arrests and file disciplinary charges if necessary.