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 happening very rapidly.  Cyclobutane exists as a puckered molecule as depicted in $\ce{A}$ and $\ce{B}$; in the ring flipping process, the molecule passes through a planar transition state.

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 that contains
   the entire molecule)

can have a dipole moment. Conformers $\ce{A}$ and $\ce{B}$ both have $\ce{C_{s}}$ symmetry and therefore do have a dipole moment; however, the planar transition state does not have a dipole moment. So at room temperature where flipping is rapid, the molecule does not have a dipole moment. If you cooled the system down to very low temperature where conformers $\ce{A}$ and $\ce{B}$ were not flipping, then you could measure a dipole moment.


  [1]: https://i.sstatic.net/BquI2.png