WASHINGTON - A needle stored with a beer can appeared to contain an extremely tiny amount of Roger Clemens’s DNA, which turned out to be good news and bad news for both sides in the perjury trial of the seven-time Cy Young Award winner.

A forensic scientist on Friday linked Clemens to cotton balls and a syringe needle saved from an alleged steroids injection 11 years ago. His testimony, laced with statistics and probabilities, was one of the last pieces of the government’s case in its effort to prove that the pitcher lied to Congress in 2008 when he denied using performance-enhancing substances.

Under cross-examination, Clemens’s lawyer tried to poke holes in the physical evidence. He got the expert to acknowledge there were “hundreds of thousands’’ of white males in the United States who could be a match for the scant amount of DNA found on the needle, and that it’s “conceivable’’ the cotton balls could have been contaminated by beer and saliva.

Prosecutors had hoped to wrap up their case heading into the long holiday weekend as the trial reached the end of its sixth week, but the DNA expert’s testimony took much longer than expected. US District Judge Reggie Walton then ended the session a half-hour early when one of the jurors learned that her mother had died.

The judge said he doesn’t expect the juror, a woman who works in law enforcement with the local public transportation authority, to return. Two jurors have previously been dismissed for sleeping, and another departure would leave only one alternate in a trial expected to last at least two more weeks.