What are the requirements and processing times for obtaining a Non-Immigrant OA visa at the Thai consulate in New York City?

Processing time for the visa ONCE you turn in all the documentation is listed here

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You need to read these requirements carefully and get EVERY document they require (and as many copies of them as they require).

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You either show monthly income of 65K baht or th equivalent using your bank statements and a letter from who ever gives you the pension or payment (year end pension or tax document etc) OR you use 800K baht or the equivalent in a bank account. It is one or the other.

Find out where you do background checks by googling New York State background check and contact some of those companies. You can down load the medical certificate from the website and if you're in thailand you can take it to the hospital or a clinic to get it signed before you go back to the US. Or if you're in the US, download the form and get your US health Care Provider to sign it