The BIG thing is WHAT thai consulate in what country are you thinking you're going to apply for the Non-B visa at :O
IF you're comin' here and going to go to the thai consulate in say Penang Malaysia to get the Non-B visa you need a police check from your country AND from thailand.
IF you're getting the visa in the US from one of the thai consulates there you just need a background check from your state.
IF you're already IN thailand you get a background check from the Police Special Branch Office in Bangkok, here;
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