Police investigating the fatal shooting of a healthcare executive in New York City are on the ground in Georgia as they hunt for his fugitive killer.

Brian Thompson of UnitedHealthcare was shot several times last week in Midtown by a gunman who fled and then apparently boarded a bus out of the city.

Law enforcement sources told the BBC’s US partner, CBS News, that officers have been despatched to the southern state and to stops along the bus route.

The search has entered its fifth day on Monday, though police have revealed neither a name nor a motive for the suspect, who was pictured several times on CCTV wearing a mask.

Much of the police activity has been focused on New York’s Central Park which seems to have formed part of the gunman’s escape route.

The lake was trawled for a second day on Sunday and a discarded backpack found nearby contained a jacket and some banknotes from the board game Monopoly but no gun, sources told CBS.

Police believe he entered the park on a bike moments after the shooting, then caught a taxi after leaving the park on the Upper West Side.

Images released over the weekend show the suspect masked in the back of the taxi heading uptown to Port Authority bus terminal near Washington Heights.

He has not been spotted on any cameras leaving the station so the presumption is that he made his escape by bus.

It is the same way he arrived in the city, 10 days before the shooting, on a Greyhound bus that originated in Atlanta.

He then checked into a hostel where he momentarily revealed his face to the receptionist, giving police their clearest image yet.

Police have not said anything about why they think he killed the 50-year-old, father-of-two Brian Thompson.

One theory is that it was an attack on the healthcare insurance system.

Bullet casings found at the scene had the words “depose,” “deny” and “delay” written on them.

This echoes the title of a book criticising the ways insurers avoid paying claims.

Thompson’s death has prompted an outpouring on social media of people sharing their stories about being denied healthcare by insurance firms.