In general liability coverage one has on a vehicle will normally extend to a trailer being pulled by the insured vehicle. Most insurance companies will cover a utility trailer used by you with the expressed or implied permission of the owner of the vehicle.
Whether other parts of an auto insurance policy would cover a trailer while it is being towed would depend upon the terms of your policy and guidelines of your insurance carrier. In many cases the trailer would need its own comprehensive or collision coverages. Some insurers would require the trailer to be listed on the declarations page of your policy to be covered.
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State insurance laws and guidelines can differ as well. For instance the Arizona Department of Insurance notes that in most cases, if a vehicle pulling a trailer is covered under your policy then the liability coverage will be extended to the trailer if you own the trailer. However, Physical Damage (comprehensive or collision) must be purchased separately. The AZ DOI also states that you will need to review your policy for exceptions.
[Let CarInsurance.com help you find affordable auto insurance now.] To make certain your trailer would be extended liability coverages by your auto insurance, and perhaps also collision coverages, contact your insurance agent and read through the terms of your policy. | 
