The Wadesville Republican says employees work late hours and often leave after armed police are gone. He noted a shooting on Statehouse grounds late one Saturday night in January.
The measure applies to employees of the House and Senate, as well as the Legislative Services Agency.
Democrats say there could be unintended consequences should an employee leave a gun unattended in an office or desk drawer.
A similar bill cleared the Senate last year but wasn't considered by the House. A vote on the bill is expected next week.