no if you have home qwner insurane you do not have to take out any other kind of insurance. it is up to the renter to take out renters insurance. i am a attonery i have been through this thousands of times. as long as you have insurance coverage on the house you can rent without any problems. i hope this helps.
most definately, you will want liability insurance to protect you and owners insurance to protect you investment in the property, as well you should require your tenant to get renters insuarance to cover their belongings and also reduce your liability.