Every painter has a preference for certain media.  Some worked almost exclusively in bodycolor and are not known to have used oil or pastel.  Louis de Carmontelle, French (1717-1806) is an example of a prolific artist who is not known to have produced a single oil painting.

Conversely, some artists stuck exclusively to oil, or to tempera, or to watercolor.

Sometimes an artist changed from one preferred medium to another at some point in his career. Jean-Baptiste Simeon Chardin, French (1699-1779) is an example of a painter who made a sudden change.  In 1771 Chardin switched from painting in oils to working in pastel. 

Checking if the medium is consistent with the painter or with a certain period in his career is an important indicator.  In some cases it can serve to eliminate a painter. To the contrary it can be one more positive element, providing a statistical probability, in support of authenticity or attribution.

Demonstrating that a painting is the authentic work of a certain artist is frequently a matter of accumulating pieces of evidence and favorable elements.  Generally, one would expect the medium to be consistent with what is known about the production of an artist.