CHICAGO (CBS) – Chicago Police say she committed suicide. Her family believes she was murdered.

As 2 Investigator Pam Zekman reports, it’s another questionable case from 2010, the year the police claimed its crime fighting techniques had dramatically reduced the city’s murder rate.

Within hours after she left El Mexico Moderno, a North Side bar, police say 38-year-old Maria Marquez parked her car near her home, then walked a mile in the middle of the night in the freezing cold, to hang herself from the branch of a tree that was three feet from the ground.

The Cook County Medical Examiner’s office ruled it was a suicide.

“My sister was a really happy person,” said her sister Areceli Rivas. “She would never have committed suicide. She would have never done that to her kids.”

A report obtained by CBS under the Freedom of Information Act indicates that, at first, the police detective on the scene thought “there was doubt” that Marquez hung herself.

According to the report, the detective told the medical investigator that, because the bottom of Marquez’s slacks covered her shoes, it appeared that someone possibly lifted her up by the legs in order to tighten the rope around her neck.

Harrison Area Detective Division Commander Anthony Riccio said, “Initially when they do arrive on the scene, detectives theorize on many different possibilities.”

But the case was closed last year as a suicide, a “non criminal death.”

“The evidence, the investigation, the interviews all lead us to think that this was a suicide,” Riccio said.

But the Marquez family hired a private detective, whose investigation raised questions.

Why didn’t police check for fingerprints on a coaxial cable he found six days later, still wrapped around a branch of the tree?

Why didn’t the police department test for DNA on a used condom he found a few feet away?

And why didn’t police pursue a tip it received about two people spotted in a van between 4 a.m. and 4:30 a.m., about the time Marquez could have been there.

Riccio said all of that was irrelevant to the suicide case.

“There’s no evidence that she was in the van or that the van was related to the incident,” Riccio said.

Another issue, why didn’t police ever question Marquez’s ex-boyfriend, who is mentioned in the police reports.

We found there was a request for an order of protection filed by his ex-wife in 2009 – in which she alleges his history of abuse included punching, slapping and hitting with objects including a rope.

And Marquez’ friends and family say that she told them he was often jealous.

“He said ‘You not going to be with me, you’re not going to be with anybody. I’m a kill you,’” Marquez’ sister Leticia Carranca recalled.

Marquez’s son told CBS 2 about a similar threat.

Finally, police were told by a friend – who was with Marquez the night she died – that Marquez ran into her ex-boyfriend at the bar.

Marquez told her friend “I just saw the devil,” recalled her sister, Arceli Rivas.

When they left, “She was afraid he might go after her.”

“Shouldn’t that have at least been pursued?” Zekman asked Riccio.

Riccio responded, “In a suicide investigation, you wouldn’t go back and try to find out why they weren’t getting along or what the problems were between a man and a woman.”

The commander says that, according to the police reports, witnesses never told police about any threats.

“This is a horrible tragedy for their family, but it is not a murder,” Riccio said.

A spokesman for the medical examiner’s office says the way Marquez died is not unusual in a suicide case. And there were no signs of violence or a struggle.

After reviewing the file, the pathologist who performed the autopsy said he sees no reason to reconsider.

Still, Riccio says that if anyone has any information about the case they should call the Harrison Area Detective Division.