New York City mayoral candidate Eric Adams’ campaign filed a lawsuit Wednesday after the city’s Board of Elections released an inaccurate vote tally in the Democratic primary. “Today we petitioned the court to preserve our right to a fair election process and to have a judge oversee and review ballots, if necessary,” his campaign said in a statement. “We are notifying the other campaigns of our lawsuit through personal service, as required by law, because they are interested parties.” Adams, the Brooklyn Borough president, called on “other campaigns to join us and petition the court as we all seek a clear and trusted conclusion to this election.” The city’s Election Board, which is run by Democrats and Republicans, on Tuesday night said it inadvertently added some 135,000 so-called “test ballots” to the count, throwing the process into disarray. The agency released the data as part of a simulation of how …