If one removes any ad hoc symmetry assumptions, the general two-Higgs-doublet model should have additional Yukawa interactions independent from fermion mass generation, in general involving flavor changing neutral Higgs couplings. These extra couplings can affect the discovered Higgs boson h through fermion loop contributions. We calculate the renormalized hZZ coupling at the one-loop level and evaluate the dependence on heavy Higgs boson mass and extra Yukawa coupling rho(u). Precision measurements at future colliders can explore the parameter space, and can give stronger bounds on rho(u) than the current bound from flavor experiments. As a side result, we find that if rho(u) cos gamma < 0, where cos gamma is the exotic Higgs component of h, the rho(u)-induced top loop contribution cancels against bosonic loop contributions, and one may have alignment without decoupling, namely sin(-gamma) similar or equal to 1, but exotic scalar bosons could have masses of several hundred GeV.