Costa Rican President Luis Guillermo Solis announced that nine people had been killed in the area of Bagaces and Upala, a town south of the Costa Rica-Nicaragua border. Earlier, he said at least six people were missing in the nearby town of Bijagua.
Solis said as much water fell on the area in a few hours as normally falls in a month, and said some people had been trapped by rising waters.
Otto made landfall on Nicaragua's Caribbean coast on Thursday as a dangerous Category 2 storm but it faded to tropical storm force before emerging over the eastern Pacific early yesterday.
Authorities in Nicaragua said the hurricane had damaged houses, but so far there were no reports of casualties. Earlier, heavy rains from the storm were blamed for three deaths in Panama.
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Otto battered Nicaragua's Corn Islands with 3.5-meter (10-foot) waves and damaged houses, but residents were all safe in refuges, said the archipelago's mayor, Cleveland Rolando Webster.
It was moving toward the west at 26 kph. It was projected to keep moving westward away from Central America, further into Pacific.
The Nicaraguan government earlier declared a state of emergency, but later reported there were no deaths directly related to the hurricane. About 400 homes in Nicaragua were damaged or destroyed.
Solis said Otto could damage the country's important coffee and agriculture sectors. Nicaragua also feared damage to coffee crops that are almost ready for harvest.