A sample of 3.73 million hadronic Z decays, recorded with the OPAL
detector at LEP in the years 1991--95, has been used to search for a
narrow resonance corresponding to the decay of the $\rm D^{*\prime\pm}(2629)$
meson into $\rm D^{*\pm}\pi^+\pi^-$. The $\rm D^{*+}$ mesons are
reconstructed in the decay channel $\rm D^{*+}\rightarrow D^0\pi^+$ with
$\rm D^0 \rightarrow K^-\pi^+$.  No evidence for a narrow 
$\rm D^{*\prime\pm} (2629)$
resonance is found. A limit on the production of $\rm D^{*\prime\pm} (2629)$ in
hadronic Z decays is derived:
\[
    f\rm (Z \rightarrow D^{*\prime\pm}(2629)) \times Br(\rm D^{*\prime +} 
\rightarrow D^{*+} \pi^+\pi^-) < 3.1 \times 10^{-3} \ \ \mathrm{(95\%\ C.L.)}
\]