The motivation behind the influence analysis is to increase the adequacy of the fitted model. Several local influence diagnostics have been proposed for different models such as linear regression, generalized linear, Weibull regression, proportional hazards etc. models by different authors on the basis of Cook's (1986) local influence method proposed for linear regression. As testing the significance of local influence is a motivating problem, in this paper we develop a likelihood ratio based test procedure for testing the significance of local influence on the parameter estimates and application is shown by fitting a logistic regression model to the Framingham Heart Study data set. This test procedure is based on the ideology of testing the equality of parameters of postulated and perturbed model. The proposed test procedure can be extended to the model having smooth and well-behaved likelihood and perturbation function.