Late on September 17, the Massachusetts House passed HB 656 by a vote of 95-58. This is the bill that lets the Governor fill a U.S. Senate vacancy almost immediately after the seat becomes vacant. The appointee would only serve until the special election, which would normally be held five months after the vacancy occurs.
As far as is known, the Massachusetts bill (if it becomes law) will be unique among the 50 states. Generally speaking, states that call a special U.S. Senate election fairly quickly after the vacancy occurs do not also provide for a gubernatorial appointment between the date of the vacancy and the special election.
Of course, most states don’t call early special elections to fill Senate vacancies. Instead, in most states, the Governor appoints someone who serves until the next regularly-scheduled Congressional election. And, sometimes the gubernatorial appointee is even permitted to serve more than two years. For example, Robert Kennedy was killed in early June 1968, and New York law permitted the man appointed by Governor Nelson Rockefeller (Charles Goodell) to serve all the way until January 1971, more than two and one-half years.