A lawsuit filed this week claims what officers are doing is unconstitutional.
The lawsuit stems from a June traffic stop of 29-year-old Erick Lopez, accused of running a stop sign.
His attorney and family say the Houston police officer held him for two hours until ICE agents arrived because he had a federal administrative immigration warrant. They say Lopez didn't have a criminal history.
"The national crime index computer system put the 700,000 non-criminal warrants in there. Before, they just had criminal warrants in the computer system, so now police can see these non-criminal immigration administrative warrants that aren't about crimes, and that's why he is held," Civil Rights Attorney Randall Kallinen said. "Many people are being held for long periods of time for these administrative warrants. These are not criminal warrants, not decided by a judge."
Houston police policy is vague, but there is no specified time limit for how long officers are required to wait for ICE to arrive.
It says as long as there is a legitimate purpose for the stop, they can hold someone as long as it's reasonably necessary. But what is reasonable?
Attorneys who filed the lawsuit say no time is reasonable under the Constitution.
Constitutional law expert Seth Chandler says in general police can only hold you at a traffic stop for the amount of time it takes to conduct the stop itself. He says if officers find you have a criminal warrant during that stop, they can hold you longer to investigate.
"The question here is whether an immigration warrant, which is not issued by a traditional judge, should be treated the same as an allegation that you were involved in a bank robbery or another violation police observed while conducting the traffic stop," Chandler said.
As this lawsuit is underway, Lopez's attorney says he was undocumented and has been deported back to Honduras.
"Erick's goal is the same. He doesn't want this to happen to anyone," Kallinen said.
Kallinen says he's trying to make this a class action lawsuit because he says there are others who Houston officers have also told during traffic stops to wait on ICE.
ABC13 has reached out to the city attorney about this suit and is awaiting a response.