Determining the ages of red-giant stars is a key problem in stellar astrophysics. One of the difficulties in this determination is to know the evolutionary state of the individual stars - i.e. have they started to burn Helium in their cores? That is the topic of this paper. Asteroseismic data provide a route to achieving this information. What we present here is a highly autonomous way of determining the evolutionary state from an analysis of the power spectrum of the light curve. The method is fast and efficient and can provide results for a large number of stars. It uses the structure of the dipole-mode oscillations, which have a mixed character in red-giant stars, to determine some measures that are used in the categorization. It does not require that all the individual components of any given mode be separately characterized. Some 6604 red-giant stars have been classified. Of these, 3566 are determined to be on the red-giant branch, 2077 are red-clump and 439 are secondary-clump stars. We do not specifically identify the low-metallicity, horizontal-branch stars. The difference between red-clump and secondary-clump stars is dependent on the manner in which Helium burning is first initiated. We discuss that the way the boundary between these classifications is set may lead to mis-categorization in a small number of stars. The remaining 522 stars were not classified either because they lacked sufficient power in the dipole modes (so-called depressed dipole modes) or because of conflicting values in the parameters.