Constrained relativistic mean field theory (RMF) has been employed for analysis of the shape phase transitions of even-even Cr52-66 isotopes. The systematic investigation of ground-state shape evolution between spherical U(5) and gamma-unstable O(6) for these nuclei has been carried out by using the potential energy curves (PECs) obtained from the effective interactions NL3*, TM1, PK1 and DD-ME2. The calculated PECs have indicated that Cr-58 can be a candidate for the critical-point nucleus with E(5) symmetry. A similar conclusion is also drawn from the calculated single-particle spectra of Cr-58 and is supported by the experimental data via observed ratios of the excitation energies. Furthermore, the gamma-independent character of Cr-58 has been pointed out by using its binding energy map in the beta-gamma plane obtained from the triaxial RMF calculations, in agreement with the condition of E(5) symmetry.