Always be sure to consult with your Consignment Pro and your insurance carrier about insurance requirements in your state and based on your type of vehicle. Generally, you will be required to maintain full coverage while your vehicle is on consignment.
Most, if not all states require licensed dealers to be bonded and insured for liability. Many dealers also carry Garage Keepers coverage in the event something happens to a customer's vehicle while in their care and custody (i.e., test drives, storage, transporting, etc.), but these policies my not cover "acts of god," such as weather, fire, flood, etc. while your vehicle is with them on consignment.
You should also contact your insurance carrier to determine if your policy has any coverage exclusions for damage or loss while on consignment.
Lastly, check to see that insurance is addressed to your satisfaction in the consignment agreement.