The "official" rule is
[A special election] 145-160 days after vacancy occurs. If a vacancy occurs after April 10 but on or before the 70th day before the regular state primary, the office shall appear on the regular state primary ballot. If a vacancy occurs after that time, the office shall appear on the state election ballot that November.
In Massachusetts a bill was passed in response to the death of Senator Edward Kennedy and his request that the current law be changed. Previous law in Massachusetts called for a special election to be held, but not until five months after the vacancy occurs. The new law retains the special election, but permits the governor to appoint a temporary successor in the interim.
In 2004, to prevent the Republican Governor from appointing a Republican, the Democrat legislature passed laws which mandated a special election. However in 2009, when Ted Kennedy died, there was a desire that the post should be filled promptly, and the law was amended so that the Governor could make an interim appointment.
The timings are further complicated by the postponement of elections due to COVID-19 restrictions. However it seems reasonably clear that
- The Governor can only appoint an interim senator.
- The Governor cannot be overruled by the legislature, but the legislature can amend the law before the Governor makes their choice.
- The timing of the special election is about 5 months after the post falls vacant.