It’s certainly possible that the dealer might have had to approach several different lenders to place your loan. Your score also drops whenever you open a new line of credit, and your score will drop because you have more open credit than you did before. Remember that your credit score is supposed to be useful to the next lender you approach, to help them predict your ability and likelihood of repaying them. And looking for credit, and recently getting new credit and making new purchases, is believed to lower the likelihood that you will be able to make the next loan you apply for.
If you get your full credit report from the credit bureaus, that will show how many hard inquiries were needed to place your auto loan. Each credit bureau has a mechanism for you to get a free credit report, but you may have to subscribe to a service or they may try to upsell you on a service contract. You can also get your credit report once a year for free from the government website www.annualcreditreport.com
