A special election was held in New York's 2nd and 3rd congressional district September 11-13, 1804 to fill a vacancy in the 9th Congress left by Representative-elect Daniel D. Tompkins (DR) resigning to accept an appointment to the New York Supreme Court.
At the time, the 2nd and 3rd districts had combined returns, functioning as a single plural district, hence, both Tompkins' initial election and this special election covered both districts.
Election returns
Mumford took his seat with the rest of the 9th Congress at the start of the 1st session.
References
New York's 2nd and 3rd congressional district special election, 1804 Wikipedia(Text) CC BY-SA