In this work, we investigate the time-dependent angular analysis of $B_s^0 \rightarrow \phi \phi$ decay to search for new physics signals via CP-violating observables. We work with a new physics Hamiltonian containing both left- and right-handed Chromomagnetic dipole operators. The hierarchy of the helicity amplitudes in this model gives us a new scheme of experimental search, which is different from the ones LHCb has used in its analysis. To illustrate this new scheme, we perform a sensitivity study using two pseudo datasets generated using LHCb's measured values. We find the sensitivity of CP-violating observables to be of the order of $5-7\%$ with the current LHCb statistics. In addition, we present a revised version of the table of coefficients of time-dependent terms in the angular decay distribution with precisely defined quantities.