Fire at a key telephone installation in San Juan cut overseas communications for Puerto Ricans and left the city’s police and hospitals without phone service. Local calls for at least 35,000 customers in the capital were disrupted by the fire, which broke out late Wednesday and knocked out a new $8-million digital complex. Firefighters battled the blaze until dawn. Authorities have not determined the cause or amount of damage of the fire. On Thursday, officials said an arson fire had been set at the telephone workers’ union headquarters a few hours after the blaze at the telecommunications center.