Also called 'cylindrical billboards'.
They work similar to standard billboards, in that you want one specific vector of the billboard's orientation (say its y-axis) to always point in the direction of the camera. The difference is you also want the laser to keep pointing in the direction of its tangent line (say the z-axis). Because of this you only have the freedom to reorient the billboard around its z-axis. So towards whatever direction you re-orient the y-axis, it needs the be orthogonal in respect to the z-axis. You can do this by orthonormalizing the camera-vertex vector in respect to the tangent vector.
So the three vectors that form a billboard matrix' orthogonal base are:
y: normalize(cameraVertex - tangent * dot(tangent, cameraVertex))