As the poster above says it changes on a daily basis. My understanding is if you are fully vaccinated no tests are needed. If you are not fully vaccinated then you must do a swab at the chiang mai airport on arrival (which i believe is free and takes only a few minutes). PCR test is only needed for international arrivals. You can check the chiang mai airport facebook page yourself for the very latest however it seems to be Thai language only.
Some larger hotels are asking for proof of vaccination however the vast majority are not. Check with the hotel directly until you find one that accommodates you. I personally wouldn't stay anywhere or eat anywhere that requires proof of vaccination even though i am indeed fully vaccinated.
Below are the current requirements.