We imported our UK car into switzerland at the beginning of the year.
The wouldn't allow us to import as personal belongings as my permit was dated before we bought the car, even though it was my wifes car and she joined me later.
You need an export cert from the uk to prove (an eu1 cert iirc) without that they will charge you import tax (in zurich anyway) based on it being a US car, regardless if it is or isn't, ours is an MG, how much more british can you get??
You'll need ALL your cars docs (V5, invoices etc etc, the more the better!!)
You'll need the certificate of conformity
You'll need to remove all non OEM gear unless you have a swîss certificate confirming they are the same or better quality as OEM (I have one for my brake discs

)
You'll need LHD headlights, convertors or adjustments are not allowed (for rhd cars, cars from the USA I have no idea)
The car will need to be swiss clean, so under the bonnet and the chassis have to be spotless, I mean really spotless, our engine bay looks brand new now, not bad for a 9 yr old car.
Noise and emissions are tested, I know people who have had to replace there car's ECU to pass this, that costs BIG money
the of course there is the test (like a UK MOT but much much stricter), we had to wait a couple of months for our test date, I know lots of people say take it, find out what it fails on then get that fixed, well thats fine if you have 4 months to kill! so we paid the mechanic to sort the car BEFORE hand, do a pre-test then for him (as he is swiss) to take the car to the test and make sure it passed. It took all afternoon and he had to argue a lot!! they where going to fail it on the speedo being out, so he got them to test it again (and it was 100% spot on) then they didn't like the bodykit (which came as standard on the uk cars) so he had to prove to them via a load of car magazines that it was standard.
Total cost around the 5k chf mark, that includes everything, tax, lights, garage work, paperwork etc etc
so much grief and hassle that we sold our other uk car and bought a swiss one instead.
Our car also has fogs and reversing lights on both sides and was fine, if it only had them on 1 side then we would have had to swap them, but again for a US car they should already be on the correct sides for here.
I have siad it before, unless your car is somthing special, or has real sentimental value to you then its just not worth importing, imports are worth bugger all here, so you'll struggle to sell it, should anything happen to it the insurance will pay out next to nothing and its a real ball ache!! every step of the process costs, and its all really really stressy!! you try arguing with a tax offical that your MG with the union jack plastered all over it, all the docs saying it british the fact they had to look up on the internet to get a value for it, is in fact british and not american all because you don't have an export cert!!