I think you'd be well within your rights to put a lock on the door. I believe that renting space you live in makes it yours, and you have similar rights just as if you rented an apartment. the landlord likely also needs to give you notice to enter for maintenance purposes etc.
If the landlord lives in the house also, it becomes rather complicated, from a practical standpoint.
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Not that I disagree with previous answer but this might be a contract issue. It is standard for there to be a clause not to alter the locks or, if done, that you need to provide the LL with a key. There are a lot of reasons why LL's need keys and also reasons why tenants need locks on their doors. Check your agreement and see what you signed on for.
Thomas A. Schaeffer, Esq. Law Office of Juarez and Schaeffer PO Box 16216, San Diego, CA 92105 (619) 804-4327 www.jslaw.org This posting is provided for "informational purposes" only and should not be relied upon as "legal advice." Nothing transmitted from this posting constitutes the establishment of an attorney-client relationship. Applicability of the legal principals discussed here may differ substantially in individual situations or in different States.
You have a right to security, and if a lock is necessary to provide that then it is allowed. However, that security is subject to your landlord's reasonable or statutory right of entry for inspection or actual emergencies.