ALICE (A Large Ion Collider Experiment) is the LHC detector dedicated to the study of nucleus-nucleus collisions, in which the formation of the Quark Gluon Plasma (QGP) is expected. Heavy quarkonia, especially the Upsilon states, are relevant for studying the QGP since they provide an essential probe of the earliest and hottest stages of heavy ion collisions. They will be measured in their dimuon decay channel in ALICE by means of the muon spectrometer. The muon spectrometer performance on Upsilon states will be presented with emphasis on the trigger efficiency and rate in Pb-Pb collisions. The Upsilon states and heavy flavor production yields will be extracted from an analysis based on a global fit of the dimuon mass spectra, at different centralities.