Yes - that is standard practice to require a lessee to carry general liability insurance to add the landlord as an additional insured.
In most states, a landowner is liable for accidents that occur on the property even when the landowner has leased it to another. It is therefore prudent for the landlord to require that the tenant obtain insurance and name the landlord as an additional insured.
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I agree, this is common in most leases today because of the liability issue.
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I'll address the second part of your question, can I ask the landowner to include my property as "additional insured" on his policy?
I see where you're coming from -- the landlord is imposing a new cost on you and you'd like something in return -- but if you buy homeowner's insurance for the sake of the liability protection, I think it will include casualty insurance for your own stuff. You wouldn't get any duplicate benefit by having the landlord insure your stuff.
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