A search for the double β processes in 106Cd was carried out at the Gran Sasso National Laboratories of the INFN (Italy) with the help of a CdWO4 crystal scintillator (215 g) enriched in 106Cd up to 66%. After 6590 h of data taking, new improved half-life limits on the double beta decay processes in 106Cd were established at the level of 1019−1021 yr; in particular, T 2νεβ + 1/2 ≥ 2.1×10 20 yr, T 2ν2β + 1/2 ≥ 4.3×10 20 yr, and T 0ν2ε 1/2 ≥ 1.0×10 21 yr. The resonant neutrinoless double electron captures to the 2718 keV, 2741 keV and 2748 keV excited states of 106Pd are restricted to T 0ν2K 1/2 ≥ 4.3 × 10 20 yr, T 0νKL1 1/2 ≥ 9.5 × 10 20 yr and T 0νKL3 1/2 ≥ 4.3 × 10 20 yr, respectively (all limits at 90% C.L.). A possible resonant enhancement of the 0ν2ε processes is estimated in the framework of the QRPA approach. The radioactive contamination of the CdWO4 crystal scintillator is reported. PACS: 29.40.Mc, 23.40.-s