United does require a health certificate, whether or not travel is in or out of USA.
Here id the link to the info they post
http://www.united.com/page/article/0,6722,1048,00.html
Please note*** all dogs travelling through the EU must have the microchip implanted.
A single kennel is limited to one pet. However, 2 kittens or puppies under 10 weeks of age are allowed in one kennel.
During taxi, takeoff and landing the pet kennel must be stowed under the seat in front of you.
The pet must remain in the closed and sealed pet kennel throughout the flight.
The total number of pet kennels allowed on a flight varies as far as the type of aircraft. It can go from 3-5 pets per aircraft, depending on how many cabins or aircraft type. I am referring to mainline, not the regional feeder airlines.
Passengers with a pet kennel may not be seated in an exit row or other restricted seats depending upon the aircraft type once again.
It is best to check in early so that you will be able to sort out all the regulations.
Always let reservations note that you will have a pet in the cabin.
Again, some of these regulations may vary slightly airline to airline. Check the airline website or call their 800 number to learn more.