Nov. 10, 2011— -- The story told to police by the mother of a missing 2-year-old "doesn't add up" and is strikingly similar to an episode of "Law and Order" that aired the day before the child disappeared, police said.
Julia Biryukova, mother of the missing child, has declined to take a polygraph test.
Biryukova has told detectives in Bellevue, Wash., she was driving her two children to Overlake Hospital Medical Center Sunday morning because her youngest child, Sky Metalwala, wasn't feeling well. She said she ran out of gas on 112th Avenue, so she and her 4-year-old daughter trekked about a mile to a nearby gas station leaving Sky in the car.
When she returned to her car, the child was gone, she told police.
Today Bellevue police Maj. Mike Johnson said police will continue their "mechanical inspection" of Biryukova's silver Acura which is housed in a secure vehicle lab.
"Julia's told us that she had difficulties with her car, she's told us that it ran out of gas, she told us that it wasn't running right, so we just want to check all of that out and see how it adds up," he said. "Eventually I expect the detectives will tell me that they want to set up another interview with Julia."
Although Biryukova did walk to the Northtowne Chevron Service on Sunday she never bought gas there, police said. Instead, she spent time walking around a wealthy neighborhood where she reportedly didn't ask anyone for help, according to the cops.
When detectives checked to see how much gas was left in her car, they found enough for her to have continued driving. Today investigators plan to drive her car, to see if it has any mechanical problems that would have forced her to leave it on the side of the road.
Police said that after Biryukova visited the gas station she called a friend who picked her up and took her back to her two-door silver Acura, where they allegedly discovered the boy was missing.
"The story doesn't add up, the whereabouts of Sky are unknown, the mother's story is falling apart, day to day," said Johnson Wednesday.
Her account bears a chilling resemblance to an episode of "Law and Order: Special Victims Unit" that aired last Saturday, the day before Sky vanished.
The episode, which police say is "strikingly similar in nature" to Biryukova's story, centered around a mother who tries to cover up the death of her child by saying he was taken from her car.
Sky's father Solomon Metalwala has agreed to take two polygraph tests, but Biryukova has refused to be tested, telling investigators that she has been too disturbed to participate.
"To be quite honest, that looks suspicious and we're puzzled by that," said Johnson.
Biryukova's lawyer declined to comment to ABC News.
Biryukova and her husband have been locked in a difficult custody battle. A judge recently denied Metalwala custody of the couple's 4-year-old but granted him limited supervised visits with his daughter.
Biryukova, however, is not permitted to have contact with her daughter who will remain in foster care until the next hearing on Dec. 5.
The couple's troubled history includes a citation for leaving Sky alone in a parked car at a Target parking lot in 2009, and angry accusations hurled at each other during their divorce proceedings.
According to the Associated Press, divorce papers say Biryukova had "severe" obsessive-compulsive disorder accompanied by 10-hour cleaning binges during which she would neglect her children. A doctor, however, testified that she was still able to care for her kids.
Police are asking the public for tips about Sky's disappearance and are offering a reward up to $1,000 for helpful information.
"We have been challenged to try to find evidence and facts to support Julia's story," Johnson said. "We want to believe Julia, we want to help her find her missing child, and we want her cooperation to do that. And at this point, the information she has given us has been problematic and has created more questions than answers."
Sky is half Indian and half Caucasian, with brown eyes and dark buzz-cut hair. He was last seen wearing a dark green hooded sweatshirt with blue and gray striped Carter's pants.
Anyone who sees a child matching this description is asked to call 911 immediately. Police are urging anyone who might have traveled along 112th Ave N.E., between I-520 and NE 24th Ave N.E., Sunday morning between 7:00 a.m. and 10:00 a.m. to call Bellevue, Wash., police at 425-452-2564 or email firstname.lastname@example.org.