New York Governor David Paterson’s current troubles — linked to his entanglement in an aide’s messy breakup, followed by accusations that he violated state ethics laws — may be a boost for Andrew Cuomo. Or maybe not.

The ambitious attorney general of New York was asked by Paterson to investigate an incident involving the governor’s alleged interference in a top aide’s domestic dispute. The controversy prompted Paterson to end his campaign for the state’s gubernatorial election coming up in November — a race Cuomo is widely expected to enter at any moment.

But the 52-year-old son of three-term New York governor Mario Cuomo may face questions about his own record — in this case,...