This paper studies the alarm response of false data injection attack in cyber-physical system under limited bandwidth constraints. Firstly, the false data injected in the actuator is modeled as unknown inputs, and the local residual generators are designed by the given $H_\infty$ performance index to generate the residual signals approaching the attack signal. Subsequently, in order to improve the alarm response, all the residual signals are quantized and then sent to the detection center under the distributed fusion framework, the optimization objective is designed and then the distributed fusion criterion are derived by solving a convex optimization problem in terms of linear matrix inequalities. Comparing with the detection method by single sensor, the detection threshold based on the distributed fusion method is more accurate, thus the alarm response is more effective and the detection time is sharply reduced. Finally, an illustrative example is used to show the effectiveness of the proposed algorithm.