Cyclobutane and its substituted derivatives readily undergo a ring flip (or ring inversion) as pictured below.

[![enter image description here][1]][1]

The barrier to ring flipping is very low, around 1.5 kcal/mole, so **at room temperature the flipping process is very rapid**.  The lowest energy conformation of cyclobutane exists in a puckered geometry as depicted in $\ce{A}$ and $\ce{B}$. In the ring flipping process, the molecule passes through a transition state where the cyclobutane ring is planar.

**Only molecules that belong to symmetry classes** (point groups) 

 - $\ce{C_{n}}$ (the molecule only contains a $\ce{C_{n}}$ axis)
 - $\ce{C_{nv}}$ (the molecule contains a $\ce{C_{n}}$ axis and a $\ce{\sigma}_{v}$ plane)
 - $\ce{C_{s}}$ (the molecule only has a plane of symmetry)

**can have a dipole moment**. 

Conformers $\ce{A}$ and $\ce{B}$ both have $\ce{C_{s}}$ symmetry (the only symmetry element is a plane that bisects the ring and contains the two cyclobutane carbons bearing the substituents) and therefore do have a dipole moment. **However**, the dipole moments of conformers $\ce{A}$ and $\ce{B}$ are equal and opposite, so when flipping is rapid the dipole moment averages out to zero. 

Therefore **at room temperature, where flipping is rapid, the molecule has zero dipole moment**. If you cooled the system down to a very low temperature where conformers $\ce{A}$ and $\ce{B}$ were not rapidly interconverting, then you could measure a non-zero dipole moment.


  [1]: https://i.sstatic.net/tNVUa.png