Police said a woman with a distinctive tattoo was Christine Belusko, who was beaten to death and strangled. No one can find her daughter.

Detectives only knew her as the Scorpion Girl for almost 30 years.

On September 20, 1991, two employees walking by found her body in a ditch across from a psychiatric hospital on Staten Island. According to news stories from the time, they thought she was a discarded mannequin at first.

The woman was handcuffed and lying on her back with her face up. She was wearing a black dress with pink trim. She wore two gold chains and a ring watch on her right finger. On her right buttock, she had a tattoo of a scorpion that was so bad that investigators at the time thought it was done by an amateur. Under her body was a hammer, the kind that mechanics use to get dents out of cars. The name “Loyd L.” was written on the handle.

Pat Savage, who started working on the case in 1993 when he was a detective on Staten Island for the Police Department, said that those were the only clues the police had about who she was and who killed her until April 2021.

But the medical examiner’s office kept a vial of her blood and some of her tissue, which helped police in New York, the F.B.I., and the Richmond County district attorney’s office figure out who she was: Christine Belusko, 30, is the only parent of her daughter, who is 2 years old. She set up Rainbow Shops stores when they first opened as part of her job.

At a news conference on Tuesday, Staten Island’s district attorney, Michael McMahon, said, “This case was followed with great sadness and public interest across the borough and beyond.”

Detectives were worried about the murder for a long time before they found out who she was. David Nilsen, the head of the detective investigators squad at the district attorney’s office, said that Ms. Belusko was strangled and hit in the head 17 times. The hammer that was found under her body was probably used to do this, he said.

Even her body was burned.

The police said they are still trying to find out who killed Ms. Belusko and what happened to her daughter, Christa Belusko, who hasn’t been seen since her mother died.

“Is she dead? “How is she?” Detective Savage, who works as an investigator for Mr. McMahon now, said this.

Mr. McMahon said that investigators hope that showing pictures of Ms. Belusko and Christa will get someone who knew the family to come forward with information that will help solve the case of the woman with the scorpion tattoo.

The child was born on August 1, 1989, so he or she would be 33 years old today. The police said they can only guess what happened to the child. The Charley Project, which keeps track of missing people, says that she was last seen a week before September 20, 1991, in Mount Airy, Pennsylvania.

Using forensic genealogy, Ms. Belusko’s name was found out. This method has helped solve hundreds of cold cases and give names to victims who had been unknown for decades.

In the case of Ms. Belusko, her blood and tissue were sent to a lab in Houston around the year 2019, and the results were checked against DNA databases. Investigators looked for possible matches in the New York and New Jersey area. They found a biological brother who was willing to give a DNA sample.

Investigators found out that Christine Belusko was born to a woman in New Jersey who had eight other kids and gave her up for adoption when she was a baby.

Detectives found out that her adoptive parents were a glass molder from Montville, New Jersey, named Frank Belusko and his secretary wife, Dorothy, who worked at an auto dealership in Boonton. Detective Savage also said that the couple had taken in another child, a son.

He said that none of them ever knew that Ms. Belusko had been killed.

Detective Savage said that Ms. Belusko moved away from her family after she found out she was adopted. She told them she was moving to Florida from Clifton, New Jersey, where she had been living with her daughter.

Investigators say she left Clifton in July 1991 and spent a short time at the Mount Airy Lodge in the Poconos.

Investigators said they couldn’t talk about her last days or why she went to Staten Island because the investigation is still going on.

The Staten Island Advance says that in the years after her death, police briefly looked into whether she might have been killed by Joel Rifkin, the Long Island serial killer who admitted to killing 17 women between 1989 and 1993.

But Mr. McMahon said that the brutal way she died shows that her killer knew her well and was angry enough to beat her badly.

“There is no indication at all that this was some sort of serial killer out on the prowl who picked her up,” Mr. McMahon said.

Ms. Belusko’s remains were buried in an unmarked grave on Hart Island off the Bronx, the site of the city’s potter’s field.

Her brother, who was in his 20s when she died, assumed she and her daughter had been living in Florida all these years and had chosen not to make contact, Detective Savage said.

Her mother died in 2000, and her father died two years later. Both obituaries named Ms. Belusko and her daughter as survivors.