Police said a shoe found near the site of where a Washington mother left her son alone in a car does not belong to her missing child.

Julia Biryukova originally told police her son, Sky Metalwala, vanished Sunday in Bellevue, Wash., when she left him unattended in her unlocked car after it ran out of gas. The mother told police she walked to a gas station with her daughter and noticed the boy was missing when they returned to the car about an hour later.

Authorities later found discovered Biryukova did not run out of gas.

A couple found the shoe four blocks from where Biryukova left her son. Police have looked at the shoe but confirmed Thursday it does not belong to Sky, according to a Fox News report.

Suspicions turn to Biryukova as investigators claim her story of what happened Sunday "doesn't add up."

"The public, I'm sure, is as frustrated as we are in the fact that mom isn't willing to come in and provide a polygraph...to be quite honest, that looks suspicious and we're puzzled by that," said Bellevue police Maj. Mike Johnson in a press conference.

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Some are speculating whether the boy's disappearance is related to a television show that aired the night before he went missing.

Johnson said the case was "strikingly similar in nature" to a "Law and Order: Special Victims Unit" episode about a child who went missing.

Authorities are asking Biryukova to disclose any information she might be hiding.

"I want to make a public invitation to Julia, through her attorney, that we are open and willing to interview her and take information whenever she's ready," Johnson said.

The disappearance of the boy occurred while his parents are in an acrimonious custody dispute. The boy's father, Solomon Metalwala, and Biryukova filed protection orders against each other as the pair continues with divorce proceedings. The pair is accusing each other of abuse and psychiatric problems.

Relatives, family friends and neighbors reportedly have not seen Sky in over than two weeks, according to police officials.