The multistate search for a troubled 13-year-old boy and his 25-year-old middle school teacher — on the run after police began investigating a relationship between the two — has moved across the border to Mexico.

A police investigator says the white Pontiac owned by the middle school teacher crossed the California border into Mexico around 11 a.m. Tuesday.

When Fernando Rodriguez called his aunt over the weekend, he asked her whether a visa or passport was required to travel to Mexico, according to court documents.

Police on Monday issued a warrant for Kelsey Peterson, who is wanted on suspicion of child abuse, child endangerment and kidnapping, authorities said.

Last week, Peterson was placed on administrative leave from Lexington Middle School, where she is a sixth-grade teacher and basketball coach, and officials confiscated her school-issued laptop.

Court documents showed authorities had recovered several e-mails and letters between the two from the school and Peterson's father. In them, Rodriguez and Peterson professed their affection for one another.

Students at the middle school told the Lexington Clipper-Herald that Rodriguez often visited Peterson's classroom and one student recalled the 13-year-old slapping Peterson on the rear when she bent over.

Click here to read the full report in the Lexington Clipper-Herald.

The Associated Press and FOXNews.com are identifying the 13-year-old even though it is alleged that he is the victim of child abuse because local officials believe it can help investigators locate the boy.

Rodriguez, while living at a home for at-risk boys in Alliance, called Peterson in letters his "Baby Gurl," and said their relationship was "just not about the sex but that it was pretty good," according to court documents.

He was sent to the home in December after a judge described the boy as an "uncontrollable" juvenile.

A month ago, Rodriguez returned to Lexington, where a neighbor of his alleges the 13-year-old had joined a local gang.

Peterson has an elementary-age child who is reportedly staying with relatives.

Click here for a report from America's Most Wanted.

The warrant charges Peterson with kidnapping, child abuse and contributing to the delinquency of a minor.

Court documents say Peterson's school-issued laptop contained letters where she said she loved the student.

Rodriguez called his mother and sister early Saturday and sent a text message to his brother, saying he was OK, police said.

The Associated Press contributed to this report.