Yes. Dogs and cats will not be an issue. Other exotic animals depend on the species so check the Costa Rican consulate or embassy.
It’s best if you bring your pet (dog and/or cat) with you when you travel to Costa Rica in the same airplane as cargo, if allowed. If you have the proper paperwork you’ll easily be able to walk them through customs with you. If you ship your pets separately as cargo you will need other paperwork such as an invoice and your pet might be in customs for a few days so it’s best to bring your pets with you in the same airplane. Check with your airline since they do have blackout dates during the summer due to the warm temperatures.
Important – You will need to present the Costa Rican customs officials a certificate of health for your pet. You can get these forms from your veterinary. Simply call them and let them know you’re taking your dog/cat to Costa Rica and they will know which forms to fill out so you can take it with you on your trip. Do not forget to do this! If you travel with your pet without the proper paperwork your pet will not be allowed into the country. It will be quarantined in these large kennels in customs for day’s even weeks for observation before they release it and you will not be able to visit your pet. Get the paperwork from your vet. It’s easy and fast and you will be able to walk your pet through customs with you into Costa Rica without issues.