Empirical likelihood (EL) combined with estimating equations (EE) provides a modern semi-parametric alternative to classical estimation techniques such as maximum likelihood estimation (MLE). This paper not only uses closed form of conditional expectation and conditional variance of Logistic equation with random perturbation to perform maximum empirical likelihood estimation (MELE) for the model parameters, but also proposes an empirical likelihood ratio statistic (ELRS) for hypotheses concerning the interesting parameter. Monte Carlo simulation results show that MELE and ELRS provide competitive performance to parametric alternatives.