MADRID (Reuters) - An attempt by the family of a Cuban dissident to get a Spanish judicial investigation into the car crash that killed him was dismissed by judges on Monday.

Relatives of Oswaldo Paya, one of the most important leaders of Cuba's small opposition and who had Spanish nationality, believe two Cuban army officials deliberately drove him off the road on the island in the summer of 2012.

Spaniard Angel Carromero, a member of Spain's People's Party, who was driving the car, was convicted by a Cuban court last year of reckless driving. On returning to Spain to serve his sentence he said that Cuban government agents had run the car off the road.

Magistrates in Madrid said on Monday they had no jurisdiction and there was no fresh evidence. The family's request was based on declarations that contradicted an initial version of events that had been accepted by the Spanish government in order to bring Carromero back to Spain to serve time, they said.

Paya's family has the right to appeal the decision.

(Reporting by Teresa Larraz; Writing by Tracy Rucinski; Editing by Sarah Morris and Robin Pomeroy)