The NA60 experiment has measured muon pair production in In-In collisions at 158 AGeV at the CERN SPS. This paper presents a high statistics measurement of φ→μ μ meson production. Differential spectra, yields, mass and width are measured as a function of centrality and compared to previous measurements in other colliding systems at the same energy. The width of the rapidity distribution is found to be constant as a function of centrality, compatible with previous results. The decay muon polar angle distribution is measured in several reference frames. No evidence of polarization is found as a function of transverse momentum and centrality. The analysis of the p T spectra shows that the φ has a small radial flow, implying a weak coupling to the medium. The T eff parameter measured in In-In collisions suggests that the high value observed in Pb-Pb in the kaon channel is difficult to reconcile with radial flow alone. The absolute yield is compared to results in Pb-Pb collisions: though significantly smaller than measured by NA50 in the muon channel, it is found to exceed the NA49 and CERES data in the kaon channel at any centrality. The mass and width are found to be compatible with the PDG values at any centrality and at any p T : no evidence for in-medium modifications is observed.