Hmm. So - yeah on a sample UA itin ex-LIR I see the "B1" surcharge (Costa Rica Boarding Tax, currently 27 USD or 15590 CRC) included in the price of the ticket. Is that the departure tax you're thinking of?
This discussion says the tax is included in most airlines' tickets:
http://costa-rica-guide.com/practica...departure-tax/
If you pay again, get a receipt clearly indicating what you paid for, and get a refund from someone.