Transition from three-dimensional to quasi-two-dimensional turbulence in a rotating frame is experimentally investigated. A decaying turbulent field is generated from oscillating a grid in a rotating water tank, and velocity measurements are performed using particle image velocimetry. The power spectrum, $E (k)$, measured in the plane normal to the rotation axis, shows a transition from the classical Kolmogorov $k^{-5/3}$ spectrum towards a $k^{-2}$ spectrum as the Rossby number is decreased. For intermediate values of Ro, a two-regime spectrum can be observed, showing a crossover between the 3D and quasi-2D regimes, in good agreement with the phenomenology proposed by Zhou [Phys. Fluids \textbf{7}:2092 (1995)]. This mixed regime takes place in a narrow band of Rossby numbers, from Ro$_\mathrm{3D} \simeq 0.15 \pm 0.10$ down to Ro$_\mathrm{Q2D} \simeq (0.10 \pm 0.03) Re^{-1/2}$.