As Fduvall posted earlier, the BVET site will give you all the information you need. Read it carefully, and follow the steps outlined in the document 'Travelling with pets - dogs, cats, and ferrets from a 3rd country'.
Just to clarify a few things other posters have said,
- You now need to have your pet microchipped (or tatoo'd during the transition phase) before importation, and the chip must conform to ISO 11784 or Annex A of ISO 11785, commonly called the 'Euro-chip'. Many US microchips do not comply with this standard; before having your dog chipped make sure your vet implants the correct chip type. You should be able to get a Euro chip in the US, but your vet may need to order it specially. Allow time for that.
(FYI, I have brought several dogs here; those from EU countries all had readable chips and I simply needed to have my vet enter their data into the ANIS (Swiss) database. Those from outside the EU (US and HK ) had to be re-chipped, as their original chips were not readable here.)
- The US is considered a country with a low risk of rabies, so see 1.3.1 of the above document for instructions. Basically, as long as your dog was kept exclusively in the US (or EU or other country at low risk) for the six months prior to importation, all that is required is that the dog is vaccinated with an inactivated vaccine as recommended by the manufacturer, at least 21 days before entry into Switzerland. The vaccine should have an efficacy of at least 1 international antigen according to WHO standards.
Because the US is on the low risk list, there is no requirement for titre testing or the 4 month waiting period. That only applies to countries on the high risk list.
- You will need a veterinary certificate signed and stamped by your vet. A sample of the certificate is available on the BVET site.
If you have any questions, contact BVET - they are the final authority, and can give you the best information. There is usually someone who speaks English on hand. I have found them to be very helpful.
Federal veterinary office (FVO):
Tel +41 (0)31 323 30 33
Fax +41 (0)31 323 85 22
E-Mail FVO
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I prefer to use a professional shipper to plan our travel and oversee the paperwork when relocating my dogs. It is a bit more expensive, but the peace of mind, knowing that an expert is dotting all i's and crossing all t's is well worth it to me. You might want to consider that option.
From experience, always fly your dog on a direct non-stop flight - even if it means driving a ways to the nearest international airport. Avoid connecting flights whenever possible - there is always a chance for mishaps when connecting flights are used.
Talk to the airline animal cargo folks to find out if there are specific crate requirements. You dog's crate should be the sturdy, non-collapsable kind (I use VariKennels), ventilated on all four sides. Your dog should be able to stand and turn around in the crate. Make sure your dog's details and your contact details are posted on the crate as well as any special instructions needed. Some planes have limited cargo space for animals, so make sure you understand how far in advance you will need to book your dog's space.
Make sure your dog is accustomed to traveling in her crate. I fit the crates out with a drip bottle, frozen. The water will melt slowly over the trip into the water tray, giving your dog enough to drink without spilling too much. It took a few days to teach my dogs to drink from a drip bottle.
Do not use sedatives!!!! They can be very dangerous during a flight. If your dog is accustomed to the crate she will settle once the plane takes off.
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Once you arrive in Switzerland, you have 10 days to register your dog with the Gemeinde and the ANIS database. You will need a Swiss vet to do the ANIS registration, so make an appointment asap once you get here. If you don't know a local vet, ask at your Gemeinde, or post on here for a recommendation.
And once you are here, have your new vet give you a Pet Passport - this is a document that contains your dog's microchip number, identification details, vaccination records, ec. (Photo optional

). You will need this to travel to other EU countries while you are here. (Be aware that while this is an EU-wide recognized document, each country has it's own entry requirements. Notably, the UK requirements are the strictest.)
And finally, do be aware of the various laws surrounding dog control issues, BSL, and your responsibilities as a dog owner in Switzerland. This is a devisive topic at present. In Basel, dog owners are required to carry personal liability insurance of minimum 3 mio coverage; this is usually part of a household contents/
Privathaftpflicht policy. You can organize that with your insurance agent.
Good luck with your move - wishing you and your dog a happy time in Switzerland.
ETA:
Just checked the BVET docs - if your dog has an incompatible US chip already implanted, it looks like you can bring your own (US) scanner to read it. I don't know of anyone who has done that, but if you want to avoid re-chipping that might be an option. I would write BVET to confirm that using your own scanner is acceptable, though, before relying on this. And have a copy of their written confirmation on hand when you bring your dog in.