Quantitative normal approximation bounds are important to obtain finite-sample, non-asymptotic inferential guarantees for various statistical problems. We derived such quantitative normal approximation results for a class of stabilizing statistics. Examples of such statistics include $k$-nearest neighbor based Entropy estimators, Euler characteristics, minimal spanning trees and Random forests. The central challenge in these problems is to handle the delicate dependency structure arising in such statistics. We handle this by utilizing the concept of stabilization, which we combine with Stein's method to establish our results. This notion of stabilization is quite universal in characterizing the local dependencies and thus provides a powerful tool for obtaining normal approximation analysis and doing finite-sample statistical inferences. Additionally, bootstrap methodology can be considered for performing practical statistical inference for the above class of problems.