A 2.5-D analytical electron Hall magnetohydrodynamic model of steady state magnetic reconnection in a collisionless compressible plasma with a constant electron temperature is developed. It is shown that as in the incompressible case, the solution of the Grad-Shafranov equation for the magnetic potential is a basis for the problem analysis. The formation of the double electric layers and layers of low-density plasma, mapping the magnetic separatrices, are investigated. It is found that the formation of depletion layers should not be governed by the out-of-plane magnetic field, but rather, the origin of these layers lies inside the electron diffusion region. The double electric layers are found to be thin separatrices-elongated sheets, whose cross sections are of the order of the electron diffusion region half width. These charged layers provide the presence of the strong electric field orthogonal to the in-plane projection of the magnetic field, which forces electrons to accelerate into the out-of-plane direction. Outside of the double electric layers, the condition of quasi-neutrality of the plasma is found to be fulfilled to high accuracy.