On June 26, Connecticut Governor M. Jodi Rell signed SB 913. It provides that when a vacancy occurs in a U.S. Senate seat, the vacancy should be filled with a special election (unless the vacancy is quite close in time to a regularly-scheduled election). Depending on the timing of the vacancy, there might or might not be primaries. If there were no time for a primary, qualified major parties would nominate by convention.
In most states, and in Connecticut until now, vacancies in U.S. Senate seats are filled by the Governor, although the appointee only serves until the next regularly-scheduled congressional election.