TWO RIVERS, Wisc. – Wisconsin authorities on Wednesday continued a weekslong search for a missing 3-year-old boy and are turning to the public for footage of a vehicle that may be connected with the child's disappearance.

Elijah Vue was last seen on Feb. 20 at the residence of Jesse Vang, a man whom investigators have described as being in a relationship with Elijah's mother, Katrina Baur, according to a criminal complaint obtained by the Manitowoc Herald Times Reporter, part of the USA TODAY Network. In an interview with police, Vang said he fell asleep for several hours that morning and, upon waking up, discovered the boy was missing and called 911.

The criminal complaint said Baur had sent her son to stay with Vang for more than a week for disciplinary reasons, a practice that had become routine over the last several months. They were both arrested within days of Elijah's disappearance. Baur, 31, faces a charge of party-to-a-crime child neglect; Vang, 39, faces a child neglect charge. Their next court appearance is scheduled for Thursday. The attorneys representing Baur and Vang did not immediately return USA TODAY's requests for comment.

Since Elijah was reported missing, a massive search effort involving local, state and federal agents has bore down on the suburban neighborhoods and rural areas of Two Rivers, a city 40 miles southeast of Green Bay. The local community has galvanized around the case and dozens of civilian volunteers have canvassed alongside law enforcement.

This week, the Two Rivers Police Department asked businesses and homeowners to check their security footage from Feb. 19, between 2 and 9 p.m., for a 1997 Nissan Altima with Wisconsin plates. On Tuesday, police said the car is not owned by Baur or Vang and that their “interest is not with the current owner of the vehicle, only in the camera footage."

Crime Stoppers in Manitowoc County, which encompasses Two Rivers, has increased the monetary reward for information leading to Elijah's discovery, or the arrest of anyone responsible for his disappearance, from $1,000 to $10,000. The FBI is also offering a $15,000 reward for relevant information.

Jesse Vang was the last person to see Elijah Vue, criminal complaint says

Vang told police he had assisted with Elijah's care and discipline on and off for about a month, according to court records. Most recently, Baur dropped Elijah off at Vang's residence on Feb. 12 with plans of returning the boy to his mother's home on Feb. 23.

On the morning Elijah was reported missing, Vang told police he saw the boy sleeping on a sofa in the living room when he woke up at 7:30 a.m. to help his own son get on the bus for school, court records said. Vang then woke Elijah up and gave him cereal to eat, but didn't change his diaper, and then had him stand next to Vang's bed and pray.

Vang said he shut the door and fell asleep at around 8 a.m., according to court records. When he woke up nearly three hours later, the boy was gone. Vang called 911 at 10:59 a.m. to report the boy missing, police said.

In an interview with investigators, Vang said he would force Elijah to stand for two to three hours without sitting as a punishment, and he would threaten Elijah with cold water, court records said. Vang described his time with Elijah as a "boot camp" and that he was trying to make the child "understand that going home is like a privilege for him."

Baur told police in her interview that she wanted Vang to teach her son "how to be a man," according to the complaint. Investigators found texts between Vang and Baur from Feb. 17 in which Vang tells Baur he was angry with Elijah for overfilling his diaper. He said he gave Elijah a cold shower, according to the complaint.

Mother lied to police about her location, court records say

When police interviewed Baur, she told them she was in Wisconsin Dells, at her primary residence, while Elijah was staying with Vang in Two Rivers from Feb. 12-20, according to the complaint.

However, location data in Baur's cellphone showed she was in Two Rivers on Feb. 14, 16 and 17.

After she was confronted with evidence, Baur later told police she visited Vang late on Feb. 16 and saw Elijah sleeping on the sofa, and she left early the next morning. No other details were given about her visit on Valentine's Day.

According to the complaint, the discrepancy in what she told police and what the cellphone data showed are the basis for the two obstructing an officer charges.

Christopher Cann reports for USA TODAY. Brand Reid reports for the Sheboygan Press. Alisa M. Schafer reports for the Herald Times Reporter.