I am a US citizen and will be in the USA in April. I am applying for a Non O visa as a first step towards obtaining a retirement visa. I need to provide documentation from the police that I have no criminal background. Is there anyone here who can tell me how to go about this in the USA?

You don't need a back ground check to get a non-o visa. You could get one from one of the honorary consulates in the states with nothing more than your passport and the $80 fee. List of them is here. http://thaiembdc.org/royal-thai-honorary-consulates-general-in-the-u-s/

You need the back ground check to apply for a OA long stay visa from the embassy in DC or one of the official consulates in New York, Chicago or Los Angeles.

In some states you can go your local police to request the back ground check. Others have a state level office that issues them and many allow you to apply for it online.

 

Does anyone know if it's still true that you can't get a single entry O visa in anywhere in the U.S.A. for the purpose of applying later for a retirement extension in Thailand?

Assuming that's still not possible, the O.P. can apply for an O-A visa in the USA which does need the criminal background report OR apply for a single entry O visa in Penang, Vientiane, or even in Thailand with the second step being the retirement extension. 

8 minutes ago, Jingthing said:

Does anyone know if it's still true that you can't get a single entry O visa in anywhere in the U.S.A. for the purpose of applying later for a retirement extension in Thailand?

Yes

They still do single entry non-o visas at honorary consulates. 

Just now, ubonjoe said:

Yes

They still do single entry non-o visas at honorary consulates. 

Thanks. I recall previously they "cracked down" on that. Moving target. Useful to the O.P. if she wants to apply for a single O while in the USA.