Connecticut Representative Linda Schofield (D-Simsbury) has introduced H5730, to provide that independent voters may vote in a party primary. Currently, Connecticut law lets each party decide for itself whether to let independent voters vote in its primary or not.
Connecticut Representative Sean J. Williams (R-Watertown) has introduced H5226, to eliminate the ability of state and local parties to choose nominees by convention, and provide that parties would nominate for all partisan office by primary. Currently, Connecticut major parties choose nominees in conventions, but anyone not chosen is free to circulate a petition and thereby force a primary for that office. But, most of the time, there are no primaries in Connecticut for most partisan offices.
Representative Williams has also introduced a bill to move the primary (for office other than President) from August to June.