Orthogonal frequency division multiplexing (OFDM) based Cell-free massive multiple-input multiple-output (CF-mMIMO) is the most promising combination that can provide uniformly better quality of service for users than cellular technology in sub-6GHz bands. To make OFDM based CF-mMIMO more cost-effective and more power-efficient, the access points (APs) should be implemented by using low-cost and low-quality transceiver hardware. However, transmitting OFDM signals with high peak-to-average power ratio (PAPR) via such hardware causes severe hardware impairments (HWI), damaging the system performance. Moreover, the PAPR reduction in CF-mMIMO-OFDM has never been studied in the open literature. In this paper, we present a smart and original PAPR reduction technique, referred to as localPAPRfree adequate for cell-free architecture. Interestingly, the proposed technique can be implemented in a distributed and scalable fashion, achieving benefits of CF-mMIMO-OFDM. Specifically, the PAPR reduction scheme is formulated as a simple convex optimization problem solved via an efficient and steepest iterative method. In addition, we present a theoretical study to analyze the downlink (DL) spectral-efficiency (SE) and energy-efficiency (EE) performance of CF-mMIMO-OFDM under power amplifier (PA) non-linearity. In an original way, we derive closed-form expressions for the DL SE and EE for the local full-pilot zero-forcing (FZF) precoding scheme with large-scale fading over independent Rayleigh block fading channels while taking into account channel estimation errors and pilot contamination. This analysis can provide important insights into the practical impact of power-efficient PA. Numerical results show that the proposed localPAPRfree algorithm offers excellent PAPR reduction performance while guaranteeing high transmission quality.