A federal jury in Alexandria found yesterday that Fairfax County and its police were not responsible for the death of a retired Navy captain who hanged himself in a county lockup following his arrest on a drunk-driving charge.

Eva Harris of Mount Vernon, the widow of Capt. Cecil Harris, who was among the leading Navy combat fliers of World War II, filed a $2 million lawsuit last December against the county, Police Chief Carroll D. Buracker and Officer Paul Crossfield, the arresting officer.

She claimed that proper measures were not taken to prevent the suicide of her husband and that he was deprived of his civil rights after he was arrested on Dec. 1, 1981.

Harris, a retired Dominion National Bank executive, was found hanging by his sweater tied to a bar above his cell door at the Groveton substation lockup about 12:15 a.m. the next day, his 65th birthday. It was about six hours after he was arrested and less than two hours after a magistrate had refused to release him into the custody of two of his sons.

During the trial, attorneys for Mrs. Harris claimed the video monitoring system at the lockup was inadequate, the audio monitor was turned off and there was no adequate procedure to prevent the suicide. They also argued that officers failed to check on Harris or pass on information about his state of mind even though Harris told them he was going to kill himself if he did not pass a Breathalyzer test.

While Harris was waiting to take the test, he told Officer Crossfield and two other officers that "if he failed the test, that was the end of his life," Crossfield testified. But, Crossfield said, "I took it to mean a change in life style."

The reading on the test was .16 blood alcohol, which in Virginia constitutes intoxication.

"This is a case about bureaucratic insensitivity," attorney David Rosenfeld told the six-member jury during his closing arguments. "Why wasn't it detected? Where were the systems, the rules, the regulations, the requirements that somebody be concerned enough to ensure the safety of those persons taken into custody by Fairfax County police?"

Attorneys for the county argued that the officers acted in good faith.

"None of those officers clearly interpreted that Harris was going to kill himself," Assistant County Attorney Peter Andreoli told the jury. Harris's behavior, he said, was consistent with the behavior of others who had been arrested on drunk-driving charges.

Moreover, Andreoli said, despite the thousands of people who have been detained at the Groveton lockup in the last 10 years, there were only three suicide attempts and one suicide before Harris'.

"If those procedures were so inadequate, there would have to be a substantial number of deaths," he told the jury.

Harris, who had been arrested three previous times for drunk driving and whose license was suspended for two years once, was described by his widow's attorneys as an alcoholic.

The jury, which heard two days of testimony, returned its verdict after deliberating for almost two hours.