Q: In our medical practice, when sharps containers are full they are taken to a storeroom to be picked up and removed on a weekly basis. Is there a regulation that states whether this room must be locked?
A: There is no federal OSHA regulation requiring a lock on the door to the regulated medical waste (RMW) storage area, only that you post signs to warn those who are about to enter.
However, state law usually takes precedence for regulated waste storage, and some states may require a locked area, especially if it is separated or outside your facility.
For your state RMW laws, go to the EPA web page “Where You Live – State Medical Waste Programs and Regulations.” 
If you are accredited or seeking accreditation, you may be required to keep RMW in a secure location, which could mean under lock and key.