Jose Gilberto Rodriguez, 46, of Houston is wanted in connection with three homicides and at least one other shooting.
Investigators believe his crime spree started on July 9 with a home invasion in the Houston area.
Harris County Sheriff Ed Gonzalez told reporters that it was too early to say what triggered the parolee's deadly "rampage".
Deputies said they also found a pistol inside the auto.
"Our hearts are heavy after hearing of another senseless act of violence at a peer mattress company in Houston on the heels of this weekend's tragic event", Steve Stagner, chief executive of Mattress Firm, said in a statement.
"We need the community to help us find this vehicle as soon as possible if you spot it do not approach it do not approach this individual contact 911 right away", Chief Acevedo says. Surveillance video showed a man, believed to be Rodriguez entering the mall and exiting out the other side. A capital murder charge is pending in the death of Allie Barrow.
"One of the calls also mentioned that an individual was out knocking on doors so there's no doubt in our mind that he meant to find his next victim", Gonzalez said, adding that a firearm was located in the vehicle.
He said another capital murder count could be filed Wednesday in the death of a man inside another mattress store on Monday.
"We are out here in the Cy-Fair/ Cypress neighborhood so it is possible that he was casing the neighborhood in search of his next victim", Gonzalez said. It appeared Rodriguez surrendered to police without a fight, KPRC reported. Authorities, who believe Rodriguez was on the hunt for his next victim when he was caught, have not offered details on the evidence allegedly linking him to the crimes.
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"We've got to up our game, because there's not enough to deal with parolees", he said.
He's the person of interest in a series of crimes, including three murders, in the Houston area.
Around 7 p.m., a Mattress Firm manager found Barrow in the back of the store.
Johnson's auto was stolen from her home and later found at a nearby mall, where surveillance video allegedly captured Rodriguez. Pamela Johnson was found dead in her home on July 13.
The Houston Chronicle reports that Rodriguez was living in a halfway house, and was working at a nearby Tyson factory, before he disappeared from the house last week and never returned.
A Houston Metro bus driver was shot along the way as well. The 22-year-old driver is listed in critical but stable condition.
Detectives said they did not yet have a motive for Rodriguez's alleged crime spree.More news: How to send spam calls straight to voicemail with Google's phone app