Insurance for sandwhich lease

If I lease a property and then re-lease or sublet to someone else, what kind of insurance should I get? Renter’s insurance?

Since the deed is still in your lessor’s name, it would simplify things greatly if your lessor just got a landlords policy and prorated it into your monthly payment to them.

If “renter’s insurance” in your state means coverage of their personal possessions, then your renters would be the ones to obtain such a policy, since they are the ones with an insurable interest in their possessions.