Police are investigating the fourth police-involved shooting in as many days.

In the latest incident, an off-duty police officer shot and killed a man who allegedly followed his wife and toddler into an apartment building to rob her Saturday night, according to an account by police officials. The police officer is assigned to the Midtown South precinct.

The officials said the officer’s wife was followed by Carlos Rios, 47, as she returned to their apartment building in the Bronx at around 11:40 p.m. with her 3-year-old daughter. On the third floor, outside of their apartment, Rios grabbed the woman and told her to open her door as he brandished a gun, police said.

The officer, whom police did not identify except to say he was a 10-year veteran, heard his wife screaming and ran to the door, police said. The officer then chased Rios to the stairwell and down to the first floor, according to the police account.

Police said shots were fired in the stairwell, and seven bullet casings from a 9-mm gun were found.

Rios was hit near his right shoulder. Officials said it was unclear if Rios had fired back at the officer, who was not hit.

Rios ran from the building after he was hit, and police say they believe he laid his gun on top of the wheel of the police officer’s car — where it was found — before collapsing. He was taken to Montefiore Hospital, where he died.

The police officer, his wife, and his daughter were treated at St. Barnabas Hospital and released. None of them were injured.

In three of the four shootings involving police officers in the past week, police fired their weapons as they were under attack, according to police officials. In the other shooting, police intervened in a drive-by after a bystander was shot and injured.