The Republican Registrar of Voters, Janice Gionfriddo, and the Democratic Registrar of Voters, Sandra Faraci, explained to me that each political party has a "Town Committee" with about 70 members. Each town committee selects candidates for each of the positions being contested in November. The standard process for getting on the ballot is to approach the Town Committee for their endorsement. If that is not successful, a potential candidate is required to collect signatures on a petition to the Secretary of State's office to force a primary election. The number of signatures must be at least 5% of the number of enrolled party members in that district.
For example, for the 33rd State Legislature district, the Democratic Town Committee chose Joe Serra and the Republican Town Committee chose Catherine Johnson. If anybody else in the 33rd district wanted to run for the nomination of either party for this office, they would have to collect signatures from the 33rd District to qualify for the ballot. Bernard Liu, in the Secretary of State's office, says that there are 5,124 registered Democrats, and 1,580 registered Republicans in the 33rd District. Thus, a potential Democratic challenger to Joe Serra this year would have required 257 signatures, while a potential Republican challenger to Catherine Johnson would have required only 79 signatures. Although Democratic primaries in the 33rd District have occurred in recent years, Gionfriddo, the Republican Registrar, could not remember the last time there was a primary on the Republican side.