@Shayan *******
you need to go to local immigration and asked for certificate of residency for purpose of car purchase. In Udon Thani, it's THB 500 for each certificate.
Your rental agreement is OK if it shows copy of the Condo title deed and owner's Thai ID card. If you use this rental agreement to get certificate of residency more than twice (eg open bank account etc), they will ask you to come back with Yellow book in future. That's what the IO said to me in UTH.