A measurement of the decay time-dependent CP-violating asymmetry in B0s→ϕϕ decays is presented, along with measurements of the T-odd triple-product asymmetries. In this decay channel, the CP-violating weak phase arises from the interference between B0s−¯B0s mixing and the loop-induced decay amplitude. Using a sample of proton-proton collision data corresponding to an integrated luminosity of 3.0  fb−1 collected with the LHCb detector, a signal yield of approximately 4000 B0s→ϕϕ decays is obtained. The CP-violating phase is measured to be ϕs=−0.17±0.15(stat)±0.03(syst)  rad. The triple-product asymmetries are measured to be AU=−0.003±0.017(stat)±0.006(syst) and AV=−0.017±0.017(stat)±0.006(syst). Results are consistent with the hypothesis of CP conservation.