In the present work we study the non-local electron-positron correlation effects. We adapt the weighted density approximation (WDA) to the problem of positron screening in the crystal lattice. We present for the effective WDA electron densities, electron-positron enhancement factors, and correlation potential of potassium, and compare them with the local density approximation (LDA) results. The LMTO-ASA method has been used to calculate the self-consistent electron charge density, which is the necessary input to the present calculation.