  Asymptotic normalization coefficients (ANCs) are fundamental nuclear
constants playing important role in nuclear reactions, nuclear structure and
nuclear astrophysics. In this paper a connection between ANCs and resonance
widths of the mirror states is established. Using Pinkston-Satchler equation
the ratio for resonance widths and ANCs of mirror nuclei is obtained in terms
of the Wronskians from the radial overlap functions and regular solutions of
the two-body Schr\"odinger equation with the short-range interaction excluded.
This ratio allows one to use microscopic overlap functions for mirror nuclei in
the internal region, where they are the most accurate, to correctly predict the
ratio of the resonance widths and ANCs for mirror nuclei, which determine the
amplitudes of the tails of the overlap functions. If the microscopic overlap
functions are not available one can express the Wronskians for the resonances
and mirror bound states in terms of the corresponding mirror two-body
potential-model wave functions. A further simplification of the Wronskians
ratio leads to the equation for the ratio of the resonance widths and mirror
ANCs, which is expressed in terms of the ratio of the two-body Coulomb
scattering wave functions at the resonance energy and at the binding energy [N.
K. Timofeyuk, R. C. Johnson, and A. M. Mukhamedzhanov, Phys. Rev. Lett. {\bf
91}, 232501 (2003]. In this paper calculations of the ratios of resonance
widths and mirror ANCs for different nuclei are presented. From this ratio one
can determine the resonance width if the mirror ANC is known and vice versa.
Comparison with available experimental ratios are done.
