No it's not required by law but it would be smart in case of building fire or if the car is stolen. First I'd find out what insurance the storage facility has. If you own the storage facility and have no insurance, you should talk to both your home/business insurance agent and your auto insurance agent to see what's best for you. No sense duplicating coverages. If it's a storage lot or building, you'd better find out how you are affected by their insurance--or they may require you to carry insurance as part of your lease.
You should also inform DMV that your car is going inoperative so that you aren't responsible for yearly registration fees.
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