UML State Diagram is used to represent the behavior of the System Under Test (SUT) when an event occurs. The state of the system is determined by the event that occurs randomly. The system state changes when the transition relationship between the States is satisfied. Test cases are generated from State Chart Diagram to test the behavior of the system. When multiple decision nodes are present in the same path, path explosion occurs. A method is proposed to generate Basis Path (BP) test cases with node coverage using Genetic Algorithm (GA) to overcome this problem. Experiments are conducted upon various Android applications and the efficiency of the algorithm is evaluated through the code coverage and the mutation analysis. Using this approach, BP test cases, Robotium test scripts are generated for 10 Android applications and observed an average of 70% reduction in the test case number concerning all path test cases. The resulted average code coverage is 74%, and Defect Removal Efficiency (DRE) is 95%. The experimental results show that the proposed method is effective when compared to other methods.