Continuity in Representation Act of 2005

Continuity in Representation Act of 2005 - (Sec. 2) Amends Federal law concerning the election of Senators and Representatives to require States to hold special elections for the House of Representatives within 49 days after a vacancy is announced by the Speaker of the House in the extraordinary circumstance that vacancies in representation from the States exceed 100. Waives the 49-day requirement if, during the 75-day period beginning on the date of the vacancy announcement, a regularly scheduled general election or another special election for the office involved is to be held.

Requires determination of the candidates who will run in the special election: (1) not later than ten days after the vacancy announcement by the political parties authorized by State law to nominate candidates; or (2) by any other method the State considers appropriate.

Sets forth requirements for judicial review of any action brought for declaratory or injunctive relief to challenge such a vacancy announcement. Requires a final decision within three days of the filing of such an action. Makes a final decision non-reviewable.

Requires a State, in conducting a special election under this Act, to ensure to the greatest extent practicable (including through the use of electronic means) that absentee ballots are transmitted to absent uniformed services voters and overseas voters not later than 15 days after the Speaker of the House announces that the vacancy exists. Requires a State to accept and process any otherwise valid ballot or other election material from an absent uniformed services voter or an overseas voter, as long as the ballot or other material is received by the appropriate State election official not later than 45 days after the State transmits it to the voter.

Applies this Act to the District of Columbia, the Commonwealth of Puerto Rico, American Samoa, Guam, and the U.S. Virgin Islands.