The short answer to your question is yes. Most lenders today require at least a credit score of about 720 for their preferential cheap rates. Since you are looking to refinance, I encourage you to sign up for membership at a local credit union (if you are not already a member). Unlike a bank who may have more constrictive guidelines on rates and payback guidelines, a credit union has different credit tiers and more flexibility set up that allows them to take a little more risk, but with higher interest costs. (Some banks may be able offer comparable terms, so the key is to look around)
Wells Fargo along with some of the other larger banks have some of the higher interest rates compared to credit unions.
I also need to mention that any bank will only loan up to a certain value - NADA book value adjusted for any overage in mileage, etc. Some lenders even go so far as to do a visual inspection, take pictures, etc to ensure that the vehicle is properly valued.
Consumer advocate for 15 years.