We study a two dimensional (2D) system of interacting quantum bosons, subjected to a continuous periodic potential in one direction. The correlation of such system exhibits a dimensional crossover between a canonical 2D behavior with Berezinski-Kosterlitz-Thouless (BKT) properties and a one-dimensional (1D) behavior when the potential is large and splits the system in essentially independent tubes. The latter is in the universality class of Tomonaga-Luttinger liquids (TLL). Using a continuous quantum Monte Carlo method, we investigate this dimensional crossover by computing longitudinal and transverse superfluid fraction as well as the superfluid correlation as a function of temperature, interactions and potential. Especially, we find the correlation function evolves from BKT to TLL type, with special intermediate behaviors appearing at the dimensional crossover. We discuss how the consequences of the dimensional crossover can be investigated in cold atomic gases experiments.