GALLATIN, Tenn. (AP) — The man who staged a St. Patrick’s Day bank robbery in a leprechaun costume and died during a police shootout also held up a bank three days before Christmas in a Santa suit, police said Thursday.

Investigators in the Nashville suburb of Gallatin said information from the FBI linked David Christopher Cotton, 20, of Brentwood to the December robbery.

FBI Supervisor Special Agent Scott Augenbaum told The Associated Press that investigators found a Santa suit at Cotton’s home, and that the suspect made similar comments during both robberies.

The man police identified as the getaway driver, 20-year-old Western Kentucky University student Jonathan Ryan Skinner, also was killed. Police said they think Cotton shot himself to death as officers surrounded the two in a field after a car and foot chase.

Patrol car video of the chase released Thursday shows one of the suspects leaning out of the passenger window of the getaway car and firing several shots at police on the street of a subdivision.

At least one round strikes the front of the car, kicking up a shower of metal and glass. Police said the shots disabled the vehicle, and the video shows a string of other police cars giving chase.

Police said the two ditched their vehicle and ran into a field near a subdivision where they died.

A friend of Cotton’s family, Rose Horton, said his parents are grieving and requested privacy. The recording on the answering machine for Albert and Annette Cotton referred calls to Horton.

‘‘They loved their son as much as any parents love their children,’’ she said. ‘‘They are thankful that no bystanders were hurt and they give their condolences to the family of the other man.’’

On his Web site Cotton describes himself as ‘‘always looking for a new adventure.’’

A YouTube video shows Cotton goofing around with a device he claims to have invented to measure whether someone is putting out good or bad vibes. He repeatedly points the device at himself and gets a ‘‘bad vibe’’ reading.

Officers don’t know how the two men were acquainted, police Lt. Kate Novitsky said.

Bob Skipper, director of Western Kentucky University media relations, confirmed that Skinner was a junior majoring in meteorology at the college in Bowling Green, Ky., about 80 miles north of Nashville. He said Skinner also was from the Nashville suburb of Brentwood. A message left on a university listing for Skinner was not immediately returned.

First State Bank was held up Wednesday afternoon by a man who wore a St. Patrick’s Day costume and carried a large-caliber gun, said Sgt. Bill Storment, a spokesman for the Gallatin Police Department.

Sharon Riehemann, manager of the Fifth Third Bank next door, said the man — wearing a green top hat, vest and shorts and a fake brown beard and wig — had come into her bank a few minutes before the robbery, but then left.

He walked toward the other bank, and then a couple of minutes later he ran out of the bank with a blue bag in his hands, Riehemann said.

No one at the bank was injured.

On Dec. 22, a man dressed in a Santa suit — including hat, beard and mustache — held up a SunTrust Bank in Nashville, demanding money from the teller at gunpoint.