Southern Indiana police fatally shot a man overnight as they were investigating a woman's complaint about a man who was harassing her and had followed her to a police station, police said Friday.

Daymon A. Hubbard, 47, of Bedford, died at a hospital after Thursday night's shooting in the city about 80 miles south of Indianapolis, Indiana State Police said.

The state agency said a woman who arrived about 10 p.m. at the Bedford Police Department to file a harassment complaint told officers that a man, later identified as Hubbard, had followed her to the police station and described his vehicle to them.

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Indiana police fatally shot a man after pursuing a suspect who followed a woman to a police station.  (Fox News)

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Five minutes later, a Bedford police officer spotted what he believed to be the man's vehicle and followed it until initiating a pursuit during which the suspect's subcompact SUV struck a patrol car.

When "the incident escalated," three Bedford police officers fired their weapons around 10:30 p.m., state police said without elaborating. Hubbard later succumbed to gunshot wounds at a Bedford hospital.

State police are investigating the fatal shooting, which it said was captured by police body cameras.

Bedford's police chief said the three officers who fired their weapons would be placed on administrative leave, a routine step following shootings involving officers.