Yes, you can bring your pet to Costa Rica. In order to do so you must have proper documentation. Each country has its own rules and procedures for “exporting” pets, so make sure you consult with your vet for the specifics.
Once in Costa Rica, you must present a health certificate stating that your pet has had the following vaccinations 30 days prior to entering the country: hepatitis, leptospirosis, distemper, parvovirus, and rabies for animals who are four months or older.However before traveling with your pet, make sure you consult with the hotels you’ll be staying at to make sure they are pet-friendly. Most hotels in Costa Rica do not have pet-friendly accommodations, although there are many that do.
Also, domestic animals are not allowed in protected areas, so your pet might not be able to come along on many of your activities. In any case, if there is any section of your trip where you foresee not being able to bring your pet along, there are some good “pet hotels” in San José where you can leave it for a few days in a nice environment (no kennels and a vet on site 24/7!).