could you upload any picture of the laser head?

As far as I remember, this laser's coming from DTK Lasersystems in Germany, and I was used to be their salesperson for France.. I think the laser's polarised.

Just take a glass plate and hold it vertically into the beam. A portion will be reflected by the glass plate.

Do the same thing by holding the plate horizontally. It there is no difference between the vertical reflected beam (in term of power) and the horizontal reflected beam, then you can say that your laser in randomly polarised.