The recent discovery of pressure induced superconductivity in the binary helimagnet CrAs has attracted much attention. How superconductivity emerges from the magnetic state and what is the mechanism of the superconducting pairing are two important issues which need to be resolved. In the present work, the suppression of magnetism and the occurrence of superconductivity in CrAs as a function of pressure ($p$) were studied by means of muon spin rotation. The magnetism remains bulk up to $psimeq3.5$~kbar while its volume fraction gradually decreases with increasing pressure until it vanishes at $psimeq$7~kbar. At 3.5 kbar superconductivity abruptly appears with its maximum $T_c simeq 1.2$~K which decreases upon increasing the pressure. In the intermediate pressure region ($3.5lesssim plesssim 7$~kbar) the superconducting and the magnetic volume fractions are spatially phase separated and compete for phase volume. Our results indicate that the less conductive magnetic phase provides additional carriers (doping) to the superconducting parts of the CrAs sample thus leading to an increase of the transition temperature ($T_c$) and of the superfluid density ($rho_s$). A scaling of $rho_s$ with $T_c^{3.2}$ as well as the phase separation between magnetism and superconductivity point to a conventional mechanism of the Cooper-pairing in CrAs.
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