An investigation is under way over a bodycam footage that appears to show a Seattle police officer laughing about a woman fatally struck by a patrol car.

Officer Daniel Auderer was responding to an incident where Jaahnavi Kandula, 23, was killed near her university.

In the video, the officer is heard suggesting the Indian student's life had "limited value" and the city should "just write a cheque".

The officer has said his comments were taken out of context.

Ms Kandula, a graduate student at the Northeastern University, was hit and killed by a police car while crossing the street on 23 January.

According to The Seattle Times, citing a police investigation report, the officer driving the car was going 74mph (119km/h) and the graduate student's body was thrown more than 100ft (30m).

Officer Auderer was called to the incident where his body camera recorded audio from a call he made to a colleague.

"But she is dead," the officer is heard saying before laughing. "No, it's a regular person. Yeah, just write a cheque," he says, before laughing again.

"Eleven thousand dollars. She was 26, anyway. She had limited value."

Mr Auderer, a Seattle Police Department union leader, was on a call with Mike Solan, the guild's president. Mr Solan's audio cannot be heard.

The Seattle Police Department released a statement on Monday saying it discovered the conversation from an employee who listened to it "in the routine course of business".

That employee was "concerned about the nature of statements" and escalated their concerns up the chain of command, according to the police statement.

Officials then handed the matter over to the Office of Police Accountability, the agency that investigates police misconduct.

The agency is looking into "the context in which" the statements were made and whether any policies had been violated, the Seattle Police Department has said.

A conservative talk radio host on KTTH-AM, Jason Rantz, reported that he had obtained a written statement from Mr Auderer saying his comments were meant to mimic how city attorneys might try to minimise liability for the woman's death.

"I laughed at the ridiculousness of how these incidents are litigated," Mr Auderer wrote, according to KTTH radio.

The Seattle Community Police Commission, another oversight agency, described the body-camera footage as "heartbreaking and shockingly insensitive".

Victoria Beach, the chair of the African American Community Advisory Council, told local news she "was shocked, had many emotions" and was "sickened about it".

"I was very disturbed that somebody could laugh about somebody that died," she said.

The King County Prosecuting Attorney's Office is conducting a criminal review of the crash.