Your homeowners insurance policy covers your property, but if you store your property off your site at a storage facility or self-storage unit, do you need additional protection? In the case of natural disasters like flood, or tornado, the facility is not likely legally responsible for your belongings.
The best way to insure specific property is to list it specifically in your policy. If you are using a storage facility for a short amount of time (such as during the time period when you are relocating to a different home), then your property is likely still covered. If you are looking for long term storage, you might consider adding the storage location to your insurance policy as an additional insured location to assure coverage for your property.
Whatever you choose, check with your insurance agency to make sure that your policy applies to items stored offsite and make sure to bring proof of insurance with you when you sign your contract for storage. You should also make sure that your items comply with any restrictions or policies of the storage facility to prevent voiding your rental contract.