Patrick Cleveland was arrested on Friday. According to the sheriff's department, Cleveland worked for Platinum Security, which provided security services for the museum.
The report on May 4 was that two men tried to steal a safe from the museum and a Dallas County security officer foiled the robbery.
The officer spotted an old pickup truck leaving the rear of the building with a safe dangling from a winch in the bed of the truck.
The officer attempted to stop the driver who then drove toward the officer, police said. The officer pulled his gun and opened fire, causing the driver to truck to hit the curb.
The crash disabled the vehicle and the two men ran away.
Detectives said they obtained information that linked Cleveland to the offense, and the investigation is ongoing and additional arrests are likely.
Cleveland has already bonded out of jail.