There is tremendous variation among state legislatures in how they fill a vacancy among their membership when it occurs.
In general, the vacancy is filled either through a special election or by appointment, and the states fall evenly into two groups. Twenty-five states fill legislative vacancies through special elections. These elections may be ordered by the governor or other official after being notified of the vacancy. The time limits for the execution of a special election vary as well. The other 25 states fill legislative vacancies through some form of appointment process, whether it be by the political party of the incumbent legislator, a board of county commissioners, the governor, the legislature or members of the same house and party as the incumbent legislator.
In addition to the variance in these laws, the provisions covering them vary as well. The vast majority of states have some provision in the state constitution for the filling of legislative vacancies. Some of these provisions state explicitly how they are to be handled while other simply state that the issue will be subject to provisions of law. In addition to constitutional provisions, most states also provide a more detailed process in statute.
Below you will find all 50 states broken down by the process used for filling legislative vacancies.