Is zero dipole moment possible in a square pyramidal complex?
A square pyridimal structure can have a dipole moment of zero, e.g. a squarepyramidal cluster of atoms of the same element would have no dipole moment. However for most cases where the bonds are polarized, the dipole moments will not cancel as they would for other symmetries (e.g. tetrahedron). So basically, most square pyramidal complexes with polarized bonds will have a net dipole.

If you have a complex in mind just calculate the dipole computationally or look at the ir spectrum.