1. Make sure it is not less than 10 days before the election.
2. Have your candidate voluntarily withdraw his name.
3. Have your candidate file a letter of withdrawal with the Secretary of State.
4. The party may then make a new nomination following party rules.
5. Wait for the Secretary of State to certify the new nominee. Once this is complete, your party has a new nominee!
6. Given the wackinesss of this race, repeat as necessary!
The relevant part of the statute is as follows:
If any party has nominated a candidate for office ... and such nominee thereafter, but prior to ten days before the opening of the polls on the day of the election for which such nomination has been made ... withdraws such nominee's name ... such party ... may make a nomination to fill such vacancy or provide for the making of such nomination as its rules prescribe.
No withdrawal, and no nomination to replace a candidate who has withdrawn, under this section shall be valid unless the candidate who has withdrawn has filed a letter of withdrawal signed by such candidate with the Secretary of the State in the case of a state or district office. ... No nomination to fill a vacancy under this section shall be valid unless it is certified to the Secretary of the State in the case of a state or district office.
Conn. Gen. Stat. § 9-460.
As far as I can see, the party cannot replace the candidate if he does not withdraw unless he either dies or becomes disqualified to hold the office for which he was nominated.