Updated

Police investigating the abduction of 6-year-old Isabel Mercedes Celis have scoured her Tucson, Ariz., home, interviewed more than 500 sex offenders and waded through 1,000-plus tips.

So far, they haven't named a suspect.

But revelations over the past week that Isabel's father, Sergio Celis, has been barred from seeing her two brothers raised questions about the focus and pace of their investigation.

On Tuesday, nearly a month since she went missing, police said for the first time that she was abducted, rather than characterizing the case as a "suspicious disappearance/possible abduction."

Authorities have been searching for the girl since her father reported her missing April 21. Family members have said they last saw her in her bedroom the night before. A window was later found open with the screen pushed aside.

A few days after the disappearance, a neighbor told KVOA-TV that she heard her dogs barking and male voices outside her bedroom window around 6:30 a.m. on the day she was reported missing. The neighbor said there were no sounds that indicated a struggle.

Police declined to comment on her account.

Authorities searched for Isabel in a three-square-mile area around her home, ponds, dry streambeds and empty houses. They also searched her house, but a judge has sealed those records until at least later this month.

Police had examined the possibility that Isabel was in Mexico because of Tucson's close proximity to the border. Federal authorities have been in touch with Mexican police officials who checked hotels, bus terminals and other businesses as they looked for her.

Meanwhile, Sergio Celis, an opera singer, sang "Ave Maria" at a May 6 benefit to raise money for the search for his daughter.

Police announced in a news release late last week that Arizona's child welfare agency was barring him from having any contact with his 10- and 14-year-old sons. On the same day, investigators released 911 recordings of him reporting his daughter missing.

He was calm while her mother's reaction was full of emotion.

Sergio Celis told a 911 operator that he believed his daughter was abducted. Asked to explain why he thought that, Celis said, he couldn't and that Isabel wasn't there when the family awoke.

"I want to report a missing person," he said, calmly. "My little girl, who is six years old. I believe she was abducted from the house."

The tone of Celis' wife, Rebecca, was frantic. "She's only six," said the mother as she cried. "Can you please hurry and get somebody over here?"

Calls to Sergio and Rebecca Celis weren't immediately returned Tuesday.

Michael Piccarreta, a criminal defense lawyer in Tucson who isn't involved in the case but has followed it, said family members are normally eliminated as possible subjects at this point in investigations. In some cases, he said, police focus on family members longer than usual.

"That doesn't mean they are guilty," Piccarreta said. "It could mean the police are having difficulty with an alternative theory."

Police spokeswoman Maria Hawke said investigators have eliminated one theory. "She didn't get up and leave the house on her own," Hawke said. She declined to discuss the evidence that led investigators to make that conclusion or reveal details about who they suspect took her.

Experts say the abduction of a child from a home is relatively rare.

Police are holding out hope that Isabel is still alive.

Tasya Peterson, a spokeswoman for the Arizona Department of Economic Security, which oversees the state's child welfare agency, declined to comment on why Sergio Celis isn't allowed to be with his two boys. She also declined to say whether there were any past calls at their home.

The Arizona Daily Star had reported early Tuesday that police concluded that Isabel was abducted.

Lynn Jones, a criminology professor at Northern Arizona University, said the public will connect the decision to prohibit Celis from seeing his sons with the 911 recordings because they were both released around the same time.

"So law enforcement, I would imagine, would have to do some work if they don't want them to be perceived together," Jones said.

Hawke said it was a coincidence that the two pieces of information were released at once and that the child welfare decision was released to keep the public informed of the investigation. News organizations had been requesting the 911 recordings, which take a while to prepare and happened to be ready on the same day as the child welfare news conference.

"People are free to form their own opinions," Hawke said.

David Pike, who lives on the same block as the Celis family and whose sons used to play with Isabel's brothers, said he is perplexed by how calm the father sounded in the 911 phone calls.

"It just struck me as odd. I get excited easily if I think one of my kids are hurt ... and then there's times I've just sat there dumbfounded. Maybe that was a dumbfounding moment for him and he wasn't able to wrap his mind around it right way," he said.

"Maybe he truly thought she was playing a game," Pike said.

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Associated Press reporter Terry Tang contributed from Phoenix.