Baby Lisa Irwin’s first birthday was marked by controversy as police denied calling the girl’s parents suspects as alleged by the family’s attorney at a press conference Friday.

Criminal defense attorney John Picerno said Kansas City Police considered Irwin’s parents, Deborah Bradley and Jeremy Irwin, to be suspects in the girl’s disappearance.

Irwin vanished from her Missouri home Oct. 3 and her parents alerted local police when the father noticed she was not in her crib.

Police deny the attorney’s claim that the parents are suspects, despite continued efforts to re-interview them, according to reports.

"We don't have any suspects," said Police Capt. Steve Young to ABC News. "We still would like to speak to them again."

The parents have not allowed police to interview them separately since Oct. 8, according to reports.

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Picerno said the parents would answer specific police questions, but with terms. The lawyer suggested they take questions from the police and relay them to the parents.

"I don't think it works that way," said Young to ABC News.

The Irwin case still has many unanswered questions as the investigation pushes into its second month.

The parents first drew suspicion when their actions seemed unusual. The mother admitted falling asleep drunk Oct. 3 as the father worked an unusual night shift.

Irwin was reported missing when the father returned home from doing electrical work at a local Starbucks at 4 a.m. on Oct. 4 and noticed she was not in her crib. The father also reported the front door unlocked, screens tampered with, the family’s cell phones missing and several lights on in the house.

The investigation appears to have stalled with the lack of new information.

Police have more questions that need answers and the family appears to have stopped cooperating with authorities as they mark a somber birthday.

"At this point, there's nothing more to be said," said Picerno.