According to Costa Rica's El Organismo de Investigación Judicial (or Judicial Investigation Department) search dogs found the partially decomposed body of a woman on Monday - almost a week after Stefaniak's family reported her missing on November 28.
Authorities also say they have detained a suspect in the case.
Family friend, Greg Zwolinsky, who is with them in Costa Rica, said he wants everyone to remember Stefaniak based on the radiance of her personality that is portrayed in pictures of her smiling.
Espinoza said the missing persons report led them to search the apartment in the San Antonio de Escazu neighbourhood, where they found "biological fluids. that are compatible with blood".
The Finding Carla Facebook page was created by her family and has been used as a place to share information about the Miami woman, who was reported missing on November 28. They received texts from her the night before around 8 p.m., but then all communication stopped.
Stefaniak as supposed to come home Thursday, but she never made it to the plane. It was discovered partially buried in plastic bags in a mountainous area. It is the last day family members heard from her. Investigators further confirmed that they had done a search of Martinez's room, but they did not provide any details about what they found. According to a timeline provided to NBC News, Stefaniak told a friend online that the power to her Airbnb cut out amid heavy rains.
On Tuesday Costa Rican officials arrested 32-year-old Bismark Espinosa Martinez, a guard at the Villa Buena Vista resort near San Jose, Costa Rica.
"That's when we knew that something's not right", Burton said.
The body was found Monday near a rental home where Carla Stefaniak stayed. The next day, after Stefaniak failed to show up at the airport, Jaime said her family took action.
Investigators performed an autopsy Tuesday, and plan to work with the Federal Bureau of Investigation to match fingerprints to formally confirm the body belongs to Stefaniak.
The body was found covered in plastic bags near an Airbnb apartment that was rented by Stefaniak, who went missing almost a week ago.
Walter Espinoza, head of Costa Rica's Judicial Investigation Department, was quoted by AP news agency as saying the Florida woman had died of head trauma.
"We all remain very hopeful and very positive that she will be found alive and safe", he said.
Bugra Demirel told the BBC: "It's a disgusting wait, and every single minute that Costa Rican officials are not showing the body is just a tremendous amount of pain on the family". I started sending her birthday messages and no-one had heard from her at all.
"Her flight wasn't until 1:30". We will always be with her and we know she will always be with us.
She later communicated with a friend via Facetime and said that she wanted to go out that night but was too exhausted.