  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
$\phi\to\mu\mu$ 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 $\phi$ 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.
