I just went through this .... I imported my 87 from canada to the US. Albeit, my car was a LHD, it was a super easy process. I would suggest you read the US Customs and Border Protection websites about importing a car to the US.
All that Customs requested from me was a letter from Toyota Motors Corp. (USA) that the Car being imported be certified by the manufacturer to meet all US Emissions and Safety standards by VIN# checking.
I called Toyota in Torrance CA, and I spoke to some very helpful folks. and in about 3weeks I had the original letter on Toyota letter head in the mail.
I took that letter, with the ownership paperwork with matching VIN# and the officers at CBP were very courteous the inspection lasted about a minute. they just checked the Vin number on windshield and door jamb to verified the title was matching and gave me all the necessary approved paperwork to take to the NYS DMV for registration and NYS title.
I hope this info helps.