The results of structural and ferromagnetic resonance (FMR) investigations of epitaxial half- metallic chromium dioxide (CrO2) thin films of thicknesses between 58 nm and 540 nm grown by chemical vapor deposition (CVD) on (100) and (110)-oriented TiO2 single crystal substrates are presented. The angular dependences of the FMR spectra in different experimental geometries were obtained. Effective magnetic anisotropies of epitaxially grown CrO2 films of different thicknesses on strain and strain-free surfaces of TiO2 substrates were estimated. The results indicate that the magnetic behavior of the CrO2 films results from a competition between the magnetocrystalline and strain anisotropies. It has been revealed that the strain anisotropy dominates in the films grown onto (100)-oriented TiO2 substrates. On the contrary, the films grown onto (110)-oriented substrates demonstrate strain-free magnetic anisotropy behavior.