An airplane belonging to rebels based in Costa Rica bombed an electrical plant and a chemical installation early today but caused no damage or injuries, the Nicaraguan government said tonight.

The Foreign Ministry charged that the plane came from Costa Rica and said a "most formal and energetic protest" was issued to the neighboring government.

The attack on the Pacific port of Puerto Sandino was claimed by the Costa Rican-based Revolutionary Democratic Alliance rebel group, the ministry said. That group also claimed previous air raids on Sept. 8 and 9.

In San Jose, a spokesman for the group, known as ARDE from its Spanish initials, said two planes dropped 250-pound bombs in the "successful" raid, The Associated Press reported. ARDE said the planes were based "somewhere in Nicaragua."

Nicaragua's statement indicated anger over what it termed Costa Rica's failure to block further military attacks by ARDE. The Foreign Ministry released the text of a 2 1/2--page protest letter from Foreign Minister Miguel D'Escoto to his Costa Rican counterpart, Fernando Volio.

"We take into account that all of the efforts and measures taken by Nicaragua, before the illustrious government of Costa Rica, to prevent the increase in those criminal actions by the counterrevolutionaries have been demonstrated to be ineffective," the letter said.

Nicaragua previously had not made public its protests to Costa Rica over air raids by the insurgents. Volio is considered to be a leading supporter in the Costa Rican government of the rebels battling the Sandinista government here.