As an interesting network architecture for future wireless communication systems, cell-free (CF) massive multiple-input multiple-output (MIMO) distributes an excess number of access points (APs) with single or multiple antennas to cooperatively communicate with several user equipments (UEs). To realize CF massive MIMO in production, hardware impairments become a crucial problem since cheaper and low-quality antennas are needed to ensure economic and energy feasibility. In this paper, we propose a framework for performance analysis in the CF massive MIMO with classical hardware distortion models. For both uplink and downlink, closed-form spectral and energy efficiency expressions are derived, respectively. Based on these results, we provide significant insights into the practical impact of hardware impairments on CF massive MIMO. For example, the impact of hardware distortion at the APs asymptotically vanishes. Furthermore, in order to ensure uniformly good service to the users, we propose a max-min power control algorithm to maximize the minimum UE rate. Via analytical and numerical results, we prove that CF massive MIMO can tolerate hardware impairments without performance reduction.