Separate from any coverage you carry with your homeowner's insurance for a duplex, you should also think about requiring any renters to have their own. Many renters expect that the owner's insurance will cover their loss but this is not true. Most property of renters, that is lost during a disaster, is the responsibility of the renter. It is important that any tenets in a rented duplex understand this part of the agreement and have their own insurance.
More importantly, anyone who needs medical attention due to an injury on your rental property should be the responsibility of the renter.
In the past, however, owners have found they have been sued by those injured on the property they own. By requiring your renter to seek out and purchase renters insurance while living in your duplex you can reduce your liability.