CT resident here. As soon as I got my VIN number, I phoned my insurance company and they emailed me an insurance card (no money needed prior to taking delivery) which I uploaded to Tesla. I decided to borrow part of the purchase price, and Tesla offered me financing with US Bank NA which I accepted. Pickup day I drove to Mt Kisco. The car had CT rear plate mounted and CT front plate with frame in the trunk (which I’d requested because I bought Snapplate brand removable front frame to install later at home). Mt Kisco had me sign NY State paperwork that I was not a NY resident so I could lawfully export car from NY to CT.
All this was in late March and although I’m CT legal and insured I never got my CT title certificate. I phoned US Bank NA and they confirmed yes they have it and they’ll be keeping it as first lienholder until I pay it off. Their “24-hour banker” emailed me a pdf of my title immediately and everything is as it should be.