Measurements of Bs2∗(5840)0 and Bs1(5830)0 mesons are performed using a data sample of proton-proton collisions corresponding to an integrated luminosity of , collected with the CMS detector at the LHC at a centre-of-mass energy of 8TeV . The analysis studies P-wave Bs0 meson decays into B(∗)+K- and B(∗)0KS0 , where the B+ and B0 mesons are identified using the decays B+→J/ψK+ and B0→J/ψK∗(892)0 . The masses of the P-wave Bs0 meson states are measured and the natural width of the Bs2∗(5840)0 state is determined. The first measurement of the mass difference between the charged and neutral B∗ mesons is also presented. The Bs2∗(5840)0 decay to B0KS0 is observed, together with a measurement of its branching fraction relative to the Bs2∗(5840)0→B+K- decay.