A gym trainer who had been dating a patron shot and killed her inside her Tennessee Avenue rowhouse on Capitol Hill and then turned the gun on himself, according to D.C. police and the woman’s parents.

The couple’s bodies were discovered Monday afternoon after a relative called police to check on the house. Police on Tuesday identified the victims as John Robinson, 37, and Desiree Cooper, 36, and classified the case as a ­murder-suicide. Few details were made public, including when the shootings occurred or how long the bodies had been inside the house in the 200 block of Tennessee Avenue NE. Cooper’s parents said they do not know of a motive.

Robinson’s relatives could not be reached. He lived in a separate house in Northeast and worked at the Results gym on G Street SE. The manager, Dekerry Davis, said Robinson had worked there for six years but declined further comment .

Cooper’s mother, Vivian ­Cooper, said her daughter met Robinson at the gym. She said her daughter, an architect in Arlington, was trying to help Robinson further his education. She said she met Robinson a few times but did not know of serious problems between the couple. “She didn’t tell me anything really bad,” her mother said.

Desiree Cooper grew up in Harrisburg, Pa., and moved to the District about a year ago. She bought the rowhouse and was renovating it between running marathons and volunteering. “She loved D.C.,” Vivian Cooper said. “She thought it was a great town. “She lived life to the fullest, and it was cut short.”