We present an experimental study of the dimensional crossover present in the extremely anisotropic superconductor ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathit{x}}$ by means of measurements of the onset field for the dissipation ${\mathit{H}}^{\mathrm{*}}$ as a function of the temperature and of the orientation ϑ between the field direction and the a,b plane. The crossover is experimentally shown to depend on the strength of the applied magnetic field in a narrow temperature range below ${\mathit{T}}_{\mathit{c}}$. The entire set of experimental data is described by a coupled-layers model, in which a decoupling can be induced by a sufficiently high magnetic field. The anisotropy ratio is found to depend strongly on the temperature and the model of coupled slabs of finite thickness quantitatively describes the data.

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