When your insured property has been re-titled in the name of your Trust, you should notify the insurance company (or agent) of the transfer and ask whether any change in the policy is required. This should apply to both casualty and liability insurance. It may be desirable for the policy to indicate that the Trust is an additional insured. The last thing you want is to give your insurance company a reason not to pay a claim.
So if you transfer ownership of your car, boat, home, etc. to your living trust, then simply contact your insurance agent/company and discuss the situation with them. Also, you can discuss this with them in advance of the transfer.