Gov. Andrew M. Cuomo plans to ask the federal government for at least $30 billion in disaster aid to help New York City and other affected areas of the state recover from the devastation of Hurricane Sandy, according to top administration officials.

In making the case for federal aid, the governor’s advisers provided a staggering inventory of need as the city and state continued to rebuild in the storm’s deadly wake: $3.5 billion to repair the region’s bridges, tunnels and subway and commuter rail lines; $1.65 billion to rebuild homes and apartment buildings; $1 billion to reimburse local governments for overtime costs of police, fire and other emergency personnel; and several billion dollars in federal loans and grants to affected businesses.

In all, Hurricane Sandy caused more than $50 billion in damage in the New York region, according to Cuomo administration officials, making it the country’s costliest storm other than Hurricane Katrina, which devastated the Gulf Coast region in 2005. That hurricane caused about $145 billion in damages, with the federal government providing about $110 billion in disaster aid, according to Cuomo officials.

In outlining the plan, Cuomo officials provided an assessment of the economic toll of the storm in New York. Businesses throughout the city and state lost $13 billion after being forced to close for days either because of damage to their property or because employees could not get to their jobs with travel restrictions widely in place, according to Cuomo aides.

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