In this letter, we consider the uplink of a cell-free Massive multiple-input multiple-output (MIMO) network where each user is decoded by a subset of access points (APs). An additional step is introduced in the cell-free Massive MIMO processing: each AP in the uplink locally implements soft MIMO detection and then shares the resulting bit log-likelihoods on the front-haul link. The decoding of the data is performed at the central processing unit (CPU), collecting the data from the APs. The non-linear processing at the APs consists of the approximate computation of the posterior density for each received data bit, exploiting only local channel state information. The proposed method offers good performance in terms of frame-error-rate and considerably lower complexity than the optimal maximum-likelihood demodulator.