If you are looking to refinance a new car, it may be difficult if you haven't had the vehicle for very long. There are rules about new car refinancing that most banks enforce before you can start a new loan.
For the most part, lenders deny refinance loans until payments have been made on the existing one for at least a year. This shows a track record of payments and gives them a good indication of how well you will pay off the loan. There are exceptions to this if you opt to switch lenders. You simply need to know what the options are with whom you work with.
Dealer loans vary in interests rates and are sometimes unfavorable to the consumer. This is why people sometimes end up owing more to the dealer than what the car is actually worth. Do the refinancing either through a credit union or bank, since they will more than likely offer much lower interest rates.
Make sure to check your credit score. If you have been perfect in paying on the loan, your credit score is likely high enough for lenders to give a better interest rate.
There really is no exact time when you should refinance a car, so it is best to look into different opportunities that might come up to see if there is a better car refinance rate available. If the rates are not right or you haven't had the car long enough to comply with lender standards, you may simply have to wait for the right time.