Heastie received seven jury duty postponements from 2005 to 2008, three times the normal amount.
Nolan announced her candidacy Wednesday, looking to replace Sheldon Silver, who was arrested last week.
The Assembly will hold an election Feb. 10 to replace Silver, who was arrested on corruption charges.
Gov. Cuomo questioned an arrangement that would allow Silver to step back from his role.
Residents fear they've lost an advocate for "getting things done" after Silver was charged with fraud.
Assembly Speaker Sheldon Silver hid more than $3 million in bribes and kickbacks, investigators say.
Rebecca Seawright, a Democrat, beat Republican David Garland in the race for the 76th District seat.
Sampson and Charles Barron won their primaries in East New York.
Farrell, 82, has represented the area in the state Assembly since 1974.
The Democratic candidates running to replace Micah Kellner will debate each other Monday night.
The primary is Sept. 9 for seats that have been open almost all year.
Two staffers were left jobless after Sheldon Silver closed the office over sex harassment allegations.
A committee resolution to let 16- and 17-year-olds serve will now go before the full City Council.
State Senate and Assembly seats in four Brooklyn districts have been vacant since January.
Kellner reportedly announced his decision at a meeting of the East Side Democratic Club last night.
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