A budget bill approved by the New York Assembly on Tuesday contains a clause that would tax purse earnings at state racetracks by 0.75 percent, a far lower rate than a tax proposed by New York Gov. Andrew Cuomo. The approval of the provision as part of the omnibus budget bill will likely open negotiations among the Assembly, Senate, and governor’s office on the size of the tax that could be assessed on horse owners. Cuomo released a budget proposal last month that called for a 3.75 percent tax on purse earnings in order to provide funding for the New York State Racing and Wagering Board, a state agency that he claimed was being “subsidized” by taxpayers. In addition to the 0.75 percent tax, the Assembly budget bill would also direct 0.475 percent of the net income from slot machines at state racetracks to the board’s budget. The New York racing industry has expressed opposition to any tax on purse earnings, contending that horse owners already lose enough money. But the New York legislature and Cuomo are searching for additional ways to raise money for state government in the face of a $10 billion deficit. New York law requires a budget to be approved by April 1, but the government has rarely met that deadline in recent years.