Zero dipole moments mean that the dipole is not formed or that the net effect is zero as it happens with many molecules. Therefore, if you are getting non-zero dipole moment, considering it to be zero will mean that the there is no effective dipole formation. As for the sign, the dipole moment is a vector and is calculated with respect to the Electric field as p = qd. Here q is the charge and d is the separation of charges with direction from negative charge to positive (-q to +q). So in my understanding, negative dipole moment will give information regarding the orientation of the dipole with respect to the applied field.

so  when i calculate it using Lippert-Mataga, Bakhshiev and Kawski equations and i get negative value of dipole moment of the ground state. what should be my interpretation ?

I actually do not know this equation. But in general the sign should give you polarity of the molecule or the direction of the applied field with respect to the dipole orientation and the value should be the magnitude of the dipole strength.