We report a measurement of the amplitude ratio \(r_S\) of \(B^0 \to D^0K^{*0}\) and \(B^0 \to \bar{D^0}K^{*0}\) decays with a model-independent Dalitz plot analysis using \(D\to K_S^0\pi^+\pi^-\) decays. Using the full data sample of \(772\times10^6\) \(B\bar{B}\) pairs collected at the \(\Upsilon(4S)\) resonance with the Belle detector at KEKB accelerator the upper limit is \(r_S < 0.87\) at the 68 % confidence level. This result is the first measurement of \(r_S\) with a model-independent Dalitz analysis, and is consistent with results from other analyses. The value of \(r_S\) indicates the sensitivity of the decay to \(\phi_3\) because the statistical uncertainty is proportional to \(1/r_S\). The \(r_S\) result is obtained from observables (\(x_\pm\), \(y_\pm\)) \begin{eqnarray} x_- &=& +0.4 ^{+1.0 +0.0}_{-0.6 -0.1} \pm0.0 \\ y_- &=& -0.6 ^{+0.8 +0.1}_{-1.0 -0.0} \pm0.1 \\ x_+ &=& +0.1 ^{+0.7 +0.0}_{-0.4 -0.1} \pm0.1 \\ y_+ &=& +0.3 ^{+0.5 +0.0}_{-0.8 -0.1} \pm0.1 \\ , \end{eqnarray} where \(x_\pm = r_S \cos(\delta_S \pm \phi_3)\), \(y_\pm = r_S \sin(\delta_S \pm \phi_3)\) and \(\phi_3 (\delta_S)\) are the weak (strong) phase difference between \(B^0 \to D^0K^{*0}\) and \(B^0 \to \bar{D^0}K^{*0}\). The first uncertainty is statistical, the second is the experimental systematic and the third is the systematic due to the uncertainties on \(c_i\) and \(s_i\) parameters measured by CLEO.