Presume you're applying for O-A? The criminal check is done in your own country, then you submit that in your application. In the UK, we have DBS for checks. There was no requirements for a Thai record check for our O-A.
My wife was in same situation, she had to go on Non B for 90 days, then moved to spouse on my Non O. This was done via Thai agent and our immigration office.
We had already tried the merry go round of KL - refused, Phnom Penh - refused. We were told to go to KL or PP by our immigration office. So we wasted about £2k doing this and still had to pay an agent.
Once she turned 50, we both got our own O-A from UK.