  Given a finite morphism $\varphi:Y\to X$ of quasi-smooth Berkovich curves
over a complete, algebraically closed field $k$ of characteristic $0$, we prove
a Riemann-Hurwitz formula relating their Euler-Poincar\'e characteristics
(calculated using De Rham cohomology of their overconvergent structure sheaf).
The main tools are $p$-adic Runge's theorem together with valuation polygons of
analytic functions. Using the results obtained, we provide another point of
view on Riemann-Hurwitz formula for finite morphisms of curves over
algebraically closed fields of positive characteristic.
