We have studied spontaneous imbibition fronts generated by capillary rise between two roughened glass plates, the separation d of which varied between 10 and 50¿¿¿¿m. Perfect agreement with Washburn¿s law was obtained. We have determined the roughness exponent ¿ of the fronts, and found ¿=0.81±0.01 for small length scales. Above a certain crossover length ¿, it reached ¿=0.58±0.04, as predicted by the quenched noise Kardar-Parisi-Zhang equation. The crossover length is found to scale with the plate separation as sqrt[d], as predicted by recent models which properly include nonlocal dynamics effects on the front. We believe this to be the first clear identification of crossover from nonlocal to local dynamics.