In the shadow of New York’s State Capitol, a 188-year-old state museum that once drew over a million visitors each year has become a confounding symbol of government neglect and mismanagement.

Over the past two decades, the state has set aside more than $75 million for gallery improvements, modernized exhibitions and a new storage facility. Yet virtually none of the money has been spent.

A third of the staff has been cut since the early 2000s. The restaurant and gift shop have closed. The operating budget is flat; the acquisitions budget is down to $36,000 a year.

And amid the institution’s fiscal challenges, federal and state officials say the state is investigating allegations that a high-ranking museum official fraudulently pursued excess federal grant money.

“We are the capital of the state, and we’ve had a tired, stagnant and stale state museum for as long as I can remember,” said Assemblywoman Patricia Fahy, whose district includes the museum in downtown Albany.

“We’re two hours north of the cultural capital of the world,” she said. “There is no reason why we should not have a better cultural museum and resource.”