I think this is a GOP pickup as of now, until we find out who the parties nominate.
http://www.politico.com/blogs/scorecard/0109/Growing_field_for_Gillibrands_seat.html?showall
On the Democratic side, Carol Schrager, a Greene County attorney who worked for Gillibrand’s campaign and raised money for Hillary Clinton, announced her candidacy Friday. Also mentioned are Larry Bulman, a union official who doubles as Saratoga County Democratic chairman; Coxsackie Town Supervisor Alex Betke; and Mike Richter, a former New York Rangers goalie whose primary residence is in Connecticut but who owns a vacation home in the Adirondacks.
The Democratic and Republican nominees for the special election will be chosen by county party chairmen, who have weighted votes based on the party enrollments in their counties — and there are 10 counties in the 20th district.
The special election will be a significant first test for House Republicans, who are trying to quickly put behind memories of the last two dismal election cycles. It would be a strong morale boost if Republicans could pick up a seat in a state where they only hold three of 31 Congressional seats.
They have reason for optimism, given the dearth of Democratic officeholders in the district and its GOP lean. But Republican operatives caution that the special election nominees are chosen by county party leaders, making it harder for the national party committee to land its favored candidate.
So I take it that there is no primary for the special election, unlike IL.