Daryl Bonelli, a friend of Shalema Gaskin, hugs the shooting victim's mother, Tanya Gaskin, left, and aunt, Lila Evans, near the crime scene Tuesday. Kevin Hagen for The Wall Street Journal

A 32-year-old mother of three was shot and killed early Tuesday morning outside a Brooklyn hospital where her 8-year-old daughter was being treated for an asthma attack, a law-enforcement official said.

As of late Tuesday, police were still searching for a suspect and a motive in the death of Shalema Gaskin, who was shot once in the neck and appeared to have all of her belongings when she was found near the back entrance of Brookdale Hospital Medical Center in the Brownsville neighborhood, the official said.

Police received a 911 call at around 3 a.m. from a passerby who saw Ms. Gaskin on the ground and arrived to find her lying face up with a gunshot wound to the neck, the official said. She was taken inside the hospital, where she was pronounced dead.

A bullet found next to her body appeared to have entered and exited her neck, the official said. She was found with what appeared to be all of her property, the official said, suggesting robbery wasn't the motive.

Ms. Gaskin, who lives four blocks from the hospital, had been there all day with her daughter, Samiyah Gaskin-Miley, and the girl's father, Mark Miley, the official said. She left around 8 p.m. Monday to go home and put their 5-year-old daughter to bed.

Family members said Ms. Gaskin returned to the hospital sometime around 2 a.m. to find Mr. Miley and Samiyah asleep in the hospital room. A nurse told the family that she had seen the woman leave the room and go downstairs.

What happened afterward is still unclear.

Police have not recovered any surveillance footage of the attack, the official said.

"I don't know what to think. I just want some help in finding who killed my daughter," said her mother, Tanya Gaskin, 50, who said her daughter was born at Brookdale Hospital.

Detectives spent much of the day combing empty lots and streets in the neighborhood for clues. A uniformed police officer kept watch over the crime scene, where blood stains remained on the hospital's blond-brick wall.

A law-enforcement official said police had been called for four domestic disturbances involving Ms. Gaskin, including one argument between her and her estranged husband. But the official said hospital staff didn't see them fighting and that the husband didn't leave his daughter's side on Monday night.

Family and friends on Tuesday erected a makeshift memorial near where Ms. Gaskin's body was found, placing votive candles, balloons, plastic flowers and one teddy bear each for Ms. Gaskin's daughters—Tamara, 18; Samiyah, 8; and Briana, 5.

The woman's aunt, Lila Evans, 47, said her niece was out of work and had been studying for a sociology degree.

"It's not fair," Ms. Evans said. "She's a good girl. She loved her kids. Everybody loved her. She had no enemies, so why would anybody hurt her?"

At Ms. Gaskin's home, a distraught Tamara Gaskin described a loving mother. "She was the greatest person on earth—grateful, loving, caring," she said. "She was my mother."

The hospital said in a statement: "This is a tragic event and our hearts go out to the family. We will continue to cooperate with authorities however we can."