ALBANY — The head of the state Republican Party has filed a complaint with the Board of Elections charging the state teachers’ union with violating election laws to boost Democrats. In a filing obtained by The Post, GOP chair Ed Cox charged that NYSUT, the state’s largest teachers’ union, and its campaign arms have exceeded contribution limits to state Senate Democrats and also share staff, which violates the law. A new law that took effect in August states that there must be a firewall of separation between PACS and groups making independent expenditures. Yet the Fund for Great Public Schools, which claims to be an independent political committee, has connections to NYSUT’s PAC, known as VOTE-COPE, according to Cox. Andrew Pallotta is listed as the treasurer of both the PAC and the Fund for Great Public Schools, according to filings viewed by The Post. Both groups also share the same address, 800 Troy-Schenectady Rd,. in Latham, N.Y. outside Albany. Since Pallotta controls the PAC, he is barred from deciding how the independent expenditure committee spends its money and on whom. Cox said that both Pallotta and NYSUT spokesman Carl Korn may be crossing the line. “The operational influence and control exercised by Andrew Pallotta and Carl Korn and the capacity in which he serves each entity strongly suggest the activities of the Fund for Great Public Schools constitute `coordination’ under NYS election law,” Cox said in the complaint. Korn has been quoted as speaking for all three groups– the union, the PAC, and the independent expenditure group, Cox pointed out. “The conduct of NYSUT, VOTE_COPE and the Fund for Great Public Schools clearly amounts to coordination and runs afoul of Section 14-107 of the NYS election law,” Cox said. Korn responded that the complaint shows the desperation of the GOP. “It’s nonsense. NYSUT follows both the letter and spirit of the law. This shows how desperate the Republicans are becoming,” he said.