More than 600 people have filed a class-action lawsuit contending they suffered health problems from the cleanup of the World Trade Center, officials said yesterday. The billion-dollar federal suit, which seeks money for medical testing and screening, cites the effects of WTC toxic diseases, according to a news release. A press conference about the case is scheduled for tomorrow at a hotel near Ground Zero. This complaint names a number of defendants who owned, managed, controlled and leased the various buildings within the WTC complex, the release said. The specific defendants were unclear, but they seemed likely to include twin towers leaseholder Larry Silverstein, the Port Authority, which owns the site, and the city. The lead lawyer in the case is David Worby, who could not be reached for comment yesterday. His firm, Worby Vecchio Edelman, LLP, represents two NYPD detectives who sued the city in June.That suit, by detective John Walcott, who has terminal cancer,