The Costa Rican hotel where Brett Gardner's family vacationed is taking precautions amid the investigation into Miller's death ... with officials telling TMZ Sports it has blocked off their room from the public as officials look into whether carbon monoxide played a factor in the tragedy.

Judicial Investigation Agency (OIJ) director Rándall Zúñiga revealed in a press conference that high levels of carbon monoxide were detected in the Arenas Del Mar Beachfront & Rainforest resort room the Gardners reserved during their trip ... and noted a "specialized machine room" was located next to their reserved space, which could have led to contamination.

The resort tells us it will continue to cooperate with the investigation ... but "out of an abundance of caution, the room in question has been blocked until further notice."

"Guest safety is our highest priority, and we regularly review our protocols to ensure we meet the highest operational standards," the resort spokesperson continued. "We take all feedback seriously and remain committed to providing a secure environment for all who stay with us."

It is expected to take a few months for Miller's autopsy to be completed.

While the family waits for answers, 14-year-old Miller's body was released back to his family. In an obituary posted to a local South Carolina newspaper, the family asked for donations to the Make-A-Wish Foundation in his memory.

"The Gardners have seen the organization's impact firsthand on numerous occasions and have always been deeply moved by the hope, strength, and inspiration each wish provides for children and families facing difficult times," the obituary read.