Authorities then located his body, which had head injuries that were likely caused by blunt objects, according to officials.
The woman hasn't yet been identified, but authorities say she has "a fair complexion, a slender build, and black hair, and stands approximately 1.60 meters tall."
At the time of the alleged homicide, the woman was wearing blue denim shorts, sandals and a white bra that had chain-like accessories on it. She was seen in security video released by police walking down a street with another woman.
The Judicial Investigation Agency in Costa Rica is asking anyone who may have information about the incident or the woman to contact 800-800-0645.
Fox News Digital has reached out to the State Department for comment.