Cummins, 50, is charged with kidnapping Thomas, 15, who has not been seen since last Monday, March 13.
They're left to believe Cummins could be staying out of sight.
Fifteen-year-old Elizabeth Thomas has been missing for almost a week. Near the same time, Cummins was captured on surveillance footage pumping gas nearby, they said. He may be driving a 2015 silver Nissan Rogue with a Tennessee license plate number 976-ZPT.
Tad Cummins handed over the title of his SUV, put up some other personal effects and walked out of the loan office with $4,500 in cash.
District Attorney Brent Cooper has issued an additional arrest warrant for a charge of aggravated kidnapping.
Jason Whatley, an attorney for Elizabeth's father, Anthony Thomas, told media this week that another student saw Cummins kissing Elizabeth on January 24.
Thomas' brother, James, said his family has repeatedly tried reaching out to her via text message, phone, and Facebook.
Thomas is fearful for his daughter's safety.
She was initially thought to be in the area of Decatur, Alabama, with Cummins.
A subsequent letter from the district to Cummins on February 3 stated that Elizabeth was in the teacher's classroom that day, which the letter said violated a previous order by the district.
Maury County Public Schools officials have been quiet about the incident. "We all love you very much and we miss you".
Tad Cummins formerly taught at the Culleoka Unit School.
The school district did not immediately respond to ABC News' request for comment.
"He had told her that he had been in the Federal Bureau of Investigation and Central Intelligence Agency". She was last seen wearing a flannel shirt and black leggings, investigators said. The student was transferred out of Cummins' class. They say they suspended Cummins on February 6 for insubordination.
Maury County is south of Nashville.
James Thomas said his father "is devastated".
Asked how Anthony Thomas is holding up, the lawyer said he's sad, anxious and suffering from high blood pressure.
"Tad, this is not you". This is not who you are... No matter how far you've gone or what's happening right now, God's grace is sufficient for you and He wants you to come home. I'd also like to state for Mr. Cummins that there is a provision that says, if the offender voluntarily releases the victim, or if he provides information that leads to her safe return, that will be weighed in his favor.
"Investigative efforts, over the past few days, continue to reveal a troubling pattern of behavior on the park of Cummins, and indicates he potentially planned this abduction prior to Monday", according to the Tennessee Bureau of Investigation. It said Cummins and Elizabeth denied a kiss took place and that the teacher said Elizabeth is "a really good friend" who comes to see him "when she needs someone to calm her down". Investigators say she was kidnapped by her former teacher.
A Tennessee teacher, fired last week, is now on the run with a 15-year-old student. I believe it's clear at this point that her removal by him is unlawful.