Generally, it’s recommended that you always call the police so that there’s a police report/accident report on file. If you’re ever in doubt about whether you should call the police, it’s better to be safe than sorry. You never know — the other driver might become uncooperative after initially agreeing to settle things privately, or there may be injuries even if you can’t see or feel them.
If you want to learn more about how to handle a fender bender, check out this article: https://getjerry.com/advice/what-to-do-after-a-fender-bender-by-rochelle-miller-hernandez.