What is the process for obtaining a police clearance letter for a Thai OA visa as a U.S. citizen?

There is a form on there website you will need to fill out. And get fingerprint at your local police station with a certified check for 18 dollars. This is the website

I'll send you a link as to how I got mine.

Why not ask the local office of the FBI. Isn't that the obvious and logical choice.

Get the non O instead. No mandatory health insurance or criminal checks. Yes you need to deposit 800,000 in a Thai bank, but if you send 65,000 baht per month, you can withdraw the 800,000 when you get your second 12 month extension.

All depends on your reason to enter Thailand. Tourist? Enter for 60 days exempt of visa. Or get a Non O based on what reason you want to go there, no police check or mandatory insurance.

why would you go via the Non-O/A route? The 90-days single entry Non-Imm-O visa is much less complicated, has no mandatory health insurance requirement, no police clearance requirement. Only when going from the 90-days stay permit to the one-year extension of stay, the 800,000 THB which you would need on your home bank account for the application to the Non-O/A visa, needs to be deposited in a Thai bank account in your name instead. That's the only difference. If you can't afford the loss of interest of funds at home compared to the low interest for funds in a Thai bank, you should rethink your retirement plan. You might also not afford to ring the bell in any bar after you lost "4-wins" for three consecutive streaks

Try to reach out to your local FBI office or local precinct