BY Adam Lisberg and Glenn Blain

Gov. Paterson plans to delay another $1.5 billion in school aid to keep the cash-strapped state from going broke next month.

Budget Division boss Robert Megna said the school money must be held back because the state faces a $1 billion cash shortfall next month – and needs the school money to pay the bills.

Still, team Paterson finds itself in a pickle: State law requires the school aid to be handed out by June 1.

Paterson will seek approval from the Legislature next week to circumvent the deadline.

But it’s not all grim news for school systems. Another pot of school cash – $2.1 billion – that has been held back since March will finally be doled out in June.

“It’s a step forward because they need this money, but they really need the full complement of state aid,” state School Boards Associations David Albert said of the $1.5 billion installment Paterson is withholding.

Paterson is holding back on the school cash as lawmakers work to close a $9.2 billion budget gap and finalize a spending plan – one that’s 45 days late.

Assembly Speaker Sheldon Silver Friday ripped Paterson for a lack of leadership and excluding the Legislature “from any meaningful dialogue” on the state’s overdue budget.

And he made a joke at Paterson’s expense.

Silver opened his speech to the Downtown-Lower Manhattan Association by mimicking his previous criticism of Ground Zero rebuilding effort.

“There’s a gaping hole that still has not been addressed. That we are where we are after this much time is an embarrassment. We cannot allow the current impasse to go on,” he riffed.

“That’s about all I’m going to say about the state budget process for the time being,” he said to laughter.

Team Paterson didn’t think it was funny.

“If the Assembly is ready to act, then they should pass a budget on Monday,” said Paterson spokesman Morgan Hook.