Authorities said Leavy was wanted on an outstanding federal material witness warrant.
U.S. Magistrate Oswald Parada late Monday ordered Leavy and Tinnemeyer turned over to the U.S. Marshals Service. Under a federal statute, they can be held for a "reasonable amount of time" until a deposition can be taken or they testify under oath.
Leavy and Tinnemeyer have not been charged in the case. Their attorney Joan Politeo declined to comment.
The warrants and affidavits in the case are under seal, said Natalie Collins, a spokeswoman for the U.S. attorney's office in Las Vegas.
Cole was dropped off in a Las Vegas neighborhood late Saturday and investigators have been speaking to him about what may have happened during his nearly four days in captivity.
Police have said his grandfather may have stolen millions of dollars from drug dealers, but they have declined to elaborate and haven't said whether the kidnappers sought a ransom.
Messages left at a number believed to be for the Tinnemeyer home in Las Vegas were not returned. Las Vegas police said they were not sure whether Tinnemeyer had a lawyer.
Police said Monday they interviewed "several persons of interest" in hopes of gaining clues to the identity of gunmen who abducted the boy last week. Two gunmen posed as police officers, bound Cole's mother and her boyfriend, then took the boy last Wednesday, authorities have said.
The boy was dropped off Saturday night in a residential neighborhood near downtown Las Vegas and was noticed by a bus driver taking disabled passengers to their homes.
At a police news conference, bus driver Julio Diaz said his attention was drawn to a little boy wandering alone at 10:30 p.m.
"It got my attention that a boy like that would be ... wandering alone," Diaz said.
Diaz said Cole came to the bus and asked if Diaz could take him home. Diaz said he did not immediately recognize the boy as missing but he thought "something was not right."
"He said he was left there. That's when I realized it was a police matter," Diaz said.
The driver took the blond, blue-eyed first-grader onto the bus and contacted police. The child said he had been dropped off just a few minutes before.
"The good thing, he wasn't shy about asking for help. I think he knew that he came to the right person," Diaz said.
Police Capt. Vincent Cannito said police have served "several" search warrants and had "dozens of leads" but added that police were not ready to name any suspects. In addition to the two abductors, police say a third person also was involved.
Cannito said authorities continued to search for Jesus Gastelum, a Mexican citizen whom Cannito said also used the name Ferdinand Gastelum.
Gastelum, who is in his mid-30s, is believed to be in Las Vegas or Southern California, police have said. Cannito declined to identify any of the other "persons of interest."
Cannito would not say whether another person of interest in police custody Saturday had been released.
At an earlier news conference, the father, Robert Puffinburger, cried and thanked police and neighbors for helping to bring his son home.
"I'm just so glad he's safe," Robert Puffinburger said.
Neither police nor Cole's father would comment on Cole's mother or Tinnemeyer, a carpenter who filed for bankruptcy in 2001.
Associated Press writers Kathleen Hennessey in Las Vegas and Greg Risling in Los Angeles contributed to this report.