  Aims: For the first time we investigate the role of the grain surface
chemistry in the Horsehead Photo-dissociation region (PDR). Methods: We
performed deep observations of several H2CO rotational lines toward the PDR and
its associated dense-core in the Horsehead nebula, where the dust is cold ($\Td
\simeq 20-30$ K). We complemented these observations with a map of the p-H2CO
$~3_{03}-2_{02}$ line at 218.2 GHz (with 12" angular resolution). We determine
the H2CO abundances using a detailed radiative transfer analysis and compare
these results with PDR models that include either pure gas-phase chemistry or
both gas-phase and grain surface chemistry. Results: The H2CO abundances
($\simeq 2-3 \times 10^{-10}$) with respect to H-nuclei are similar in the PDR
and dense-core. In the dense-core the pure gas-phase chemistry model reproduces
the observed H2CO abundance. Thus, surface processes do not contribute
significantly to the gas-phase H2CO abundance in the core. In contrast, the
formation of H2CO on the surface of dust grains and subsequent photo-desorption
into the gas-phase are needed in the PDR to explain the observed gas-phase H2CO
abundance, because the gas-phase chemistry alone does not produce enough H2CO.
The assignments of different formation routes are strengthen by the different
measured ortho-to-para ratio of H2CO: the dense-core displays the equilibrium
value ($\sim3$) while the PDR displays an out-of-equilibrium value ($\sim2$).
Conclusions: Photo-desorption of H2CO ices is an efficient mechanism to release
a significant amount of gas-phase H2CO into the Horsehead PDR.
