Dhanush Sai, 20, a resident of Andhra Pradesh, fell off MV Boa Sorte, a vessel operated by Casino Carnival, and was still missing, police said.
A complaint was filed on Monday under penal provisions for endangering life or personal safety, police said.
The casino management said all safety measures mandated by the state government were in place on the vessel.
Dhanush, along with two other friends, had been on a holiday to Goa and on Sunday decided to visit the casino vessel, located off Panaji, police said.
"Eyewitnesses said that he slipped from the second level of the boat. It was raining and the area was slippery. His friend dived in after him, but the body could not be found," a police official said, adding that professional divers were also unable to trace Dhanush.
In a statement issued on Monday, a company official said that casino officials were fully co-operating with police.
"At this moment, our thoughts are with the family of the person who is missing. Casino Carnival follows strict code of safety," a spokesperson said, adding that all stipulated licences and safety procedures which were mandated by law were in place.