Two people died in Bagaces, a town north of the capital San Jose, and another in Upala on the border with Nicaragua, police told national television networks.
President Luis Guillermo Solis said in an overnight statement that an unspecified number of people were missing after the passage of Hurricane Otto.
The hurricane - which weakened to a tropical storm before exiting into the Pacific Ocean - dumped a months' worth of rain in just a few hours, he said.
"We are receiving a big number of incidents," he said, adding that more details would be given later once evaluations had been made.
There were no reports of casualties in Nicaragua, where several homes were damaged.
"Up to now, thank God, we haven't counted any loss of human life," the Nicaraguan government's spokesperson, First Lady Rosario Murillo, told state media.