Bellevue police have asked the mother of 2-year-old Sky Eliah Metalwala to come to the station and answer additional questions about her son's disappearance.

Bellevue police want Julia Biryukova to know that they are "open and willing to interview her and take information whenever she's ready," Maj. Mike Johnson said Thursday.

Johnson was careful to point out during two media briefings that Biryukova, 30, of Redmond, is not a suspect nor a person of interest in the disappearance of Sky. He also said police do not want to "force" the mother into answering their questions.

Nevertheless, he said, police believe "Julia holds the key" to the toddler's whereabouts.

Police have been inundated with tips and have been able to "move forward" in their investigation, primarily by eliminating a number of people in connection with the child's disappearance. Johnson said none of Biryukova's relatives or friends has shown "any resistance" to helping police.

Thursday night, Bellevue police said a toddler's shoe was found several blocks from where Sky was reported missing.

A police dog brought to the scene did not pick up Sky's scent, and the shoe looked "pretty small," police spokesman Carla Iafrate said. But police can't say for sure that it isn't Sky's shoe until further investigation is done, she said. "We want to be totally certain," she said.

Biryukova, a stay-at-home mother, told police she was driving her brother's car to Overlake Hospital Medical Center in Bellevue on Sunday morning because her son was ill. She said the car ran out of gas in the 2600 block of 112th Avenue Northeast.

She said she left her sleeping son in the unlocked car and walked with her 4-year-old daughter to get help.

She told police her son was gone when she returned to the car about an hour later.

On Wednesday, police determined the car's gas tank held enough gasoline "to run a significant distance."

The children's father, Solomon Metalwala, 36, has been interviewed by police and has volunteered to take a second polygraph test after the first was deemed inconclusive.

Police said they have not been able to speak directly with Biryukova, who has been staying since Sunday in a hotel room provided by the department. They said she is answering questions through her attorney and has declined to take a polygraph examination.

One of her attorneys, Veronica Freitas, said the Redmond woman has answered every question asked of her by investigators. Biryukova was advised by legal counsel not to take the polygraph test, Freitas said.

The boy's disappearance came two days after the mother attempted to pull out of a custody agreement that was crafted in a grueling, 11-hour mediation session, according to Metalwala's attorney, Leslie Clay Terry III.

Terry said the mother has admitted to police that the children were left alone at her apartment during that mediation.

The couple had been locked in a bitter and contentious divorce, with parties seeking protective orders against the other and both leveling accusations of abuse.

Metalwala has said that something about Biryukova's story "does not add up," a sentiment echoed by Bellevue police.

"There's something missing, and if you find out what's missing, it will lead to our child," Metalwala said earlier this week.

Suzanne and Robin Hays, of Kirkland, said Thursday they were staggered to learn the missing child was the son of their former neighbors.

Metalwala and Biryukova lived in the 12500 block of Northeast 80th Place in Kirkland for about six months when Biryukova was pregnant with Sky and for a short time after his birth.

At that time, they said, it was always Metalwala they saw with the children.

"He seemed very happy and nice," said Suzanne Hays. "He was good with the kids and was the one who always took them out."

Biryukova, they said, was reclusive and somewhat anti-social.

"I never saw her except when she walked to the mailbox, and even then she would keep her eyes down," said Suzanne Hays.

Police said they have been unable to find anyone who had seen Sky in the two weeks before his disappearance, but they also learned it was not uncommon for Biryukova to remain inside the home with her children for periods of time.

They also said she would leave her children at home alone for extended periods.

Christine Clarridge: 206-464-8983 or cclarridge@seattletimes.com

Information from Seattle Times archives is included in this report.