This paper presents an experimental study of a vibration-assisted dry micro-wire electrical discharge machining (${mu}$-WEDM) utilized in high precision and micro-manufacturing area. The assisted vibration was applied to the workpiece using a piezoelectric actuator, and high pressure air was injected directly into the machining gap through a nozzle. Investigation experiments were performed to estimate the importance of input parameters and it was observed from experiment results that the width (kerf) of the cutting slot and the machining time were significantly affected by the air injection pressure and input energy. Moreover, it was also observed that there exists an optimal relationship between the machining time and input parameters including the air pressure and vibration frequency and amplitude. Central composite design based experiments were also carried out, and empirical models of the machining time and cutting slot kerf have been developed using the response surface methodology to analyze and optimize the process.