As the owner of a rental property you could be held liable for known and unknown conditions at the property. In most cases your fire/liability insurance policy will cover you adequately. You should discuss with your insurance company the amount of recommended limits for your situation.
If you use a professional property manager,most have an indemnity clause in their management agreement that places basic liability for all acts on the owner. Insurance companies know this and most will willingly name the property manager as either additional insured or name the manager as an interested party to the policy at no extra cost. This is important to do as you want the insurance company to protect both the owner and the property manager in the unlikely event of a lawsuit. Some insurance companies refuse to name or cover the property manager. This is unfortunate. The property owner can obtain insurance for the liabilities at the property, but a property manager may not be able to obtain insurance on a property they do not own. Even if they could, most property managers base their management rates on fact that the owner provides the insurance.
It makes sense for the owner to provide insurance, after all, the owner owns the property and has to have the coverage whether they have a professional property manager or not. Having a property manager actually reduces the owners risk, so insurance companies are being short sighted by not covering the property manager. Again, most do provide this coverage.
In most cases, just acting with common sense and acting quickly will lessen the likelihood of a lawsuit.