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Authorities investigating the disappearance of a 2-year-old Washington state boy said his mother's account of what happened is strangely similar to a popular TV crime show.

Sky Metalwala, 2, was reported missing Sunday morning by his mother after she discovered him missing from her car in Bellevue, Wash.

Julia Biryukova told police that she was driving her sick son to a hospital when she ran out of gas. She claimed she left the boy buckled into his car seat, sleeping, while she and her 4-year-old daughter walked to a Chevron gas station, about a mile away. When the two returned to the unlocked car, the child was gone, according to Biryukova.

Police said Biryukova's story "doesn't add up," and is very similar to an episode of "Law & Order: SVU," which aired a day before the child disappeared.

"I've heard about the 'Law and Order: SVU' episode that has great similarity to this case. I heard that it aired Saturday, the day before the disappearance of Sky," Bellevue Police Maj. Mike Johnson told reporters Thursday.

"I know that there are several folks up in the operations center of the command post that have taken a look at that episode, and have commented that it is strikingly similar in nature," Johnson said.

Biryukova has so far refused to take a lie detector test, according to authorities. The child's father, Solomon Metalwala, is expected to take a second polygraph test after the first one was ruled inconclusive.

Biryukova and Metalwala are in the midst of a bitter divorce battle.

In court documents, Metalwala said his wife suffers from mental illness and had dreams about killing the couple's children, according to Fox affiliate KCPQ-TV.

Biryukova has accused Metalwala of domestic violence, claiming he assaulted her in front of the children in December 2009.

Police have said they suspect foul play in the disappearance of Sky, who is of Indian and Caucasian descent with brown eyes and dark hair. He was last seen wearing a dark green hooded sweatshirt and blue and gray-striped pants, according to his mother.

Authorities have said they found no gas can in their investigation. The also found that Biryukova's car had plenty of gas in it when its fuel tank was checked.

"There was a sufficient amount of gas in that vehicle to run it for a considerable distance," Johnson said.

Biryukova had previously been cited for leaving a child unattended in a vehicle. In 2009, Redmond police cited Biryukova and Metalwala for leaving a child unattended in a vehicle. The case was dismissed after they agreed to probation, community service and a 10-week parenting class.

Fox News' Dan Springer contributed to this report.