“My credit union will be cheaper” and “the dealer can get the best rate” are both conclusions you can reach too early. Until you have actual offers, you have a preference.
There is good reason to contact a bank or credit union before shopping. An offer gives you a basis for comparison. There is also good reason to let the dealer compete. The finance office may have access to lenders or a manufacturer program that works well for the vehicle and borrower.
Dealer-arranged financing often involves a bank, credit union, or finance company behind the transaction anyway. The practical question is what terms reach you.
Understand how the dealer is paid
A lender may quote a rate to the dealership, called the buy rate, and the dealership may offer a higher contract rate that compensates it for arranging the financing. The CFPB explains this distinction and advises buyers to compare outside offers.
That is a reason to examine the quote. It does not tell you whether a particular dealer offer beats the one you brought. Compare the same amount, term, and cash down wherever possible. If a product is included in one offer, account for its price before attributing the payment difference to the rate.
Manufacturer promotions need another look. A subsidized rate may have eligibility conditions, and an offer may require choosing between a finance promotion and a cash incentive. Compare the actual alternatives available to you. A low APR attached to a higher amount financed needs arithmetic, not enthusiasm.
A straightforward approach works well: obtain an outside offer, explain it to the dealer, and give the finance office a chance to improve it. If the outside lender remains better, understand its funding process and timing before delivery.
You do not owe either source the loan because it was convenient or because you have used it before. Choose the terms that work best for this purchase.