Anomalous contributions to the electric and magnetic dipole moments of the τ lepton from new physics scenarios have brought renewed interest in the development of new charge-parity violating signatures in τ-pair production at Belle II energies, and also at higher energies of the Large Hadron Collider and the Future Circular Collider. In this paper, we discuss the effects of spin correlations, including transverse degrees of freedom, in the τ-pair production and decay. These studies include calculating analytical formulas, obtaining numerical results, and building semirealistic observables sensitive to the transverse spin correlations induced by the dipole moments of the τ lepton. The effects of such anomalous contributions to the dipole moments are introduced on top of precision simulations of e−e+→τ−τ+, qq¯→τ−τ+ and γγ→τ−τ+ processes, involving multibody final states. The τ decays are simulated along with radiative corrections, in particular electroweak box contributions of WW and ZZ exchanges are taken into account. Respective extensions of the Standard Model amplitudes and the reweighting algorithms are implemented into the Monte Carlo, which is used to simulate τ-pair production in e−e+ collisions, and the aupinner program, which is used to reweight events with τ pair produced in pp collisions. Published by the American Physical Society 2024