A Queens nursing-home director billed taxpayer-funded Medicaid for his . . . Lexus!

The 240-bed Elmhurst Care Center overcharged Medicaid by some $1.65 million — including more than $105,000 in expenses for a Lexus used by Executive Director Mark Persaud and another vehicle assigned to the marketing executive, Gov. Cuomo’s Medicaid probers claim.

The six-year audit, conducted by state Office of Medicaid Inspector General James Cox, concluded that expensing the program for the hospital administrator’s luxury vehicle was beyond the pale.

“Costs pertaining to luxury automobiles are not related to patient care. Consequently, disallowances were necessary,” said the OMIG audit, which examined billings from 2000 to 2006.

Elmhurst Care insisted the expenses were aboveboard.