How can you find out for certain which State officials leading various State offices are in appointed positions? (Beyond just assuming they are.)
The State Secretary of State’s office should have a little publication, quite likely available online, along the lines of “Your State Government and You” – and it will describe or list which officials are elected and which appointed.
In New York, for example, the Governor appoints the heads of all executive Departments – mostly called “Commissioners” – except the State Comptroller and Attorney General, which are elected. In North Carolina, there are something like six or eight department heads which make up the “Council of State,” which has some specific constitutional duties under certain circumstances. The Council of State member Secretaries are elected, the others appointed by the Gov.
I believe the pattern is like that in each state – certain officials, ones who need independence of action, get elected by the voters; the others, who need to work as a team to carry out the winning Governor’s platform, are appointed by him.