An analytical solution of the two-density Omsteia-Zernike (OZ) equation with the associative mean spherical approximation (AMSA) closure is obtained for the shielded sticky point (SSP) electrolyte model. The model is presented by the dimerizing version of the restricted primitive electrolyte model with dimerization which occurs due to the site-site sticky interaction at distances less than the ionic hard-core diameter. The present version of the AMSA is an extension of the associative MSA proposed recently [M. Holovko and Yu. Kalyuzhnyi, Mol. Phys. 73, 1145 (1991)]. It is demonstrated that, in the limit of complete association, the present two-density OZ equation reduces to the Chandler-Silbey-Ladanyi equation. Predictions from the AMSA in this limit are compared with those obtained by Monte Carlo simulations.