We provide the first-ever performance evaluation of orthogonal time frequency space (OTFS) modulation in cell-free massive multiple-input multiple-output (MIMO) systems. To investigate trade-off between performance and overhead, we apply embedded pilot-aided and superimposed pilot-based channel estimation methods. We then derive a closed-form expression for the individual user downlink and uplink spectral efficiencies as a function of the numbers of APs, users and delay-Doppler domain channel estimate parameters. Based on these analytical results, we also present new scaling laws that the AP's and user's transmit power should satisfy, to sustain a desirable quality of service. It is found that when the number of APs, $M_a$, grows without bound, we can reduce the transmit power of each user and AP proportionally to $1/M_a$ and $1/M_a^2$, respectively, during the uplink and downlink phases. We compare the OTFS performance with that of orthogonal frequency division multiplexing (OFDM) at high-mobility conditions. Our findings reveal that with shadowing correlation, OTFS modulation with embedded pilot-based channel estimation provides $30$-folds gain over the OFDM counterpart in terms of $95\%$-likely per-user downlink rate. Finally, with superimposed pilot-based channel estimation, the increase in the per-user throughput is more pronounced at the median rates over the correlated shadowing channels.