  We have performed a search for neutrinoless $\beta^{+}\hspace{-0.2em}EC$
decay of $^{120}$Te using the final CUORE-0 data release. We describe a new
analysis method for the simultaneous fit of signatures with different event
topology, and of data subsets with different signal efficiency, obtaining a
limit on the half-life of the decay of $T_{1/2}>1.6\cdot10^{21}$ yr at $90\%$
CI. Combining this with results from Cuoricino, a predecessor experiment, we
obtain the strongest limit to date, corresponding to $T_{1/2}>2.7\cdot10^{21}$
yr at $90\%$ CI.
