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Some identities in law in terms of planar complex valued Ornstein-Uhlenbeckprocesses $(Z_{t}=X_{t}+iY_{t},t\geq0)$ including planar Brownian motion areestablished and shown to be equivalent to the well known Bougerol identity forlinear Brownian motion:$(\beta_{t},t\geq0)$: for any fixed $u>0$:\sinh(\beta_{u}) \stackrel{(law)}{=}\hat{\beta}_{(\int^{u}_{0}ds\exp(2\beta_{s}))}. These identities in law for2-dimensional processes allow to study the distributions of hitting times$T^{\theta}_{c}\equiv\inf\{t:\theta_{t} =c \}, (c>0)$,$T^{\theta}_{-d,c}\equiv\inf\{t:\theta_{t}\notin(-d,c) \}, (c,d>0)$ and morespecifically of $T^{\theta}_{-c,c}\equiv\inf\{t:\theta_{t}\notin(-c,c) \},(c>0)$ of the continuous winding processes$\theta_{t}=\mathrm{Im}(\int^{t}_{0}\frac{dZ_{s}}{Z_{s}}), t\geq0$ of complexOrnstein-Uhlenbeck processes.

On hitting times of the winding processes of planar Brownian motion and of Ornstein-Uhlenbeck processes, via Bougerol's identity