NEW YORK – The battle lines in Harvey Weinstein’s criminal case grew sharper on Tuesday as the movie mogul pleaded not guilty to rape and criminal sex act charges in New York and his lawyer promised a fight. A lawyer for Weinstein signaled he would use legal challenges to try to derail the case before it reaches trial, even as signs surfaced that prosecutors are showing their own resolve by continuing to interview potential victims. The not guilty plea marked Weinstein’s first court appearance since surrendering May 25 after months of accusations by dozens of women alleging sexual and other misconduct. Weinstein limped from an SUV and was escorted past a big crowd of journalists before spending a few minutes answering a series of yes and no questions from the judge asking if he understood his rights. He didn’t stop to speak with journalists or respond to shouted questions and was back in his waiting SUV in just 40 minutes.