COPPELL, Texas -- Autopsy reports show the Coppell mayor's 19-year-old daughter was shot from behind and the mayor shot herself in the forehead.

The Dallas County medical examiner released records on Tuesday showing Corinne Peters was shot in the back of the neck from several feet away.

The two women were found dead in their home earlier this month after Jayne Peters didn't show up for a City Council meeting. Coppell, a city of 40,000 people, is about 15 miles northwest of Dallas.

Multiple media outlets around the Dallas-Fort Worth area reported Wednesday that city officials announced an anonymous donor gave the city $10,000 to cover the mayor's charges on her city credit card. The announcement coincided with the release of a city investigation that shows the mayor charged more than $6,300 in personal and unexplained expenses on the card.

The note accompanying the donation says, "Please use these dollars to reimburse the city for any and all credit card charges of Jayne Peters, with any remainder to go to the city."

The city's investigation found that only $1,348 items charged on her card were legitimate. Nearly $2,000 of the questioned charges were made two weeks before Peters apparently shot herself and her 19-year-old daughter in their home. They included payments for rental cars, gas, restaurants, clothes and groceries.

City officials have said they had been questioning the mayor about her use of the city credit card in the months before her death.

The medical examiner determined the daughter's death was a homicide and the mayor's a suicide. The records do not definitively state that the mayor killed her daughter, although investigators believe she did. The autopsies also did not say who died first.

The women didn't have alcohol or drugs in their systems when they died, the reports said. However, Jayne Peters did have two patches of the powerful painkiller fentanyl, a drug commonly used by cancer patients, on her back. The medical examiner's office found no evidence of the painkiller in her system, however. Nor did it find that the mayor had cancer.

Steve Thomas, deputy chief of police for the Coppell Police Department, said police are still gathering details before they close the investigation, including a time of death, information from the mayor's computer files and test results from outside agencies.

"All the information we have received thus far points to that (murder/suicide), but until the investigation is complete, it is a death investigation," he said.

The bullet that killed the mayor's daughter struck her in the back of the neck and came out through her right cheekbone, the reports said. Her body was found in the laundry room wrapped in towels on the first floor of the family's two-story home.

The mayor's body was found in the upstairs bathroom with a "do not resuscitate" note, one of four notes left behind for first responders.

Another note said the two were still grieving over the 2008 death from cancer of their husband and father.

"My sweet, sweet Corinne had grown completely inconsolable. She had learned to hide her feelings from her friends. But the two of us were lost, alone and afraid. Corinne just kept on asking, 'Why won't God let me die?' We hadn't slept at all and neither one of us could stop crying when we were together," read a typed note that police found in the kitchen.

Jayne Peters was a contract software developer who served on the City Council for a decade. She was elected mayor in 2009.

Her daughter had recently told friends that she was heading to the University of Texas at Austin in the fall. Neighbors and friends said Corinne Peters was excited and had been wearing shirts with the university's Longhorn logo and colors. But a UT spokesman said the school had no record of her applying.

Thomas said a neighbor saw Corinne putting things in her car at 6 a.m. the morning before she was killed. Shortly after she placed them in the car, the elder Peters was seen taking items back into their home.