Does the cost of auto refinance outweigh the costs saved with the new deal? If you were to reduce your monthly payments this would most likely be offset by an increase in the length of the time taken to pay off the loan.
How much of your existing loan is already paid off? If you have paid off the greater part of, then it might not be worth refinancing a car loan.
Check how much your car is worth on the open market. Refinancing providers are unlikely to lend more than the present value of the vehicle.
It is important to compare and contrast interest rates offered by the various providers.
If it was a while since you took out the original finance then be prepared for the more stringent rules which lenders now apply to borrowers. You may well have to provide more information about your finances than you would have had to previously.
To qualify for the most favourable interest rates you will need a good credit score, and be up to date with the payments on the existing loan.
If you do decide to refinance a car, it is important to take the time and effort to read the accompanying documentation carefully, paying particular attention to the small print.