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Studies on double beta decay processes in $^{106}$Cd were performed by usinga cadmium tungstate scintillator enriched in $^{106}$Cd at 66%($^{106}$CdWO$_4$) with two CdWO$_4$ scintillation counters (with natural Cdcomposition). No effect was observed in the data accumulated over 26033 h. Newimproved half-life limits were set on the different channels and modes of the$^{106}$Cd double beta decay at level of $\lim T_{1/2}\sim 10^{20}-10^{22}$ yr.The limit for the two neutrino electron capture with positron emission in$^{106}$Cd to the ground state of $^{106}$Pd,$T^{2\nu\mathrm{EC}\beta^+}_{1/2}\geq2.1\times 10^{21}$ yr, was set by theanalysis of the $^{106}$CdWO$_4$ data in coincidence with the energy release511 keV in both CdWO$_4$ counters. The sensitivity approaches the theoreticalpredictions for the decay half-life that are in the range$T_{1/2}\sim10^{21}-10^{22}$ yr. The resonant neutrinoless double-electroncapture to the 2718 keV excited state of $^{106}$Pd is restricted at the levelof $T^{0\nu\mathrm{2K}}_{1/2}\geq2.9\times10^{21}$ yr

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Search for double beta decay of $^{106}$Cd with an enriched  $^{106}$CdWO$_4$ crystal scintillator in coincidence with CdWO$_4$  scintillation counters