We carried out high-sensitivity spectropolarimetric observations of the central star of the Red Rectangle proto-planetary nebula with the aim of constraining the mechanism that gives its biconical shape. The stellar light of the central binary system is linearly polarised since it is scattered on the dust particles of the nebula. Surprisingly, the linear polarisation in the continuum is aligned with one of the spikes of the biconical outflow. Also, the observed Balmer lines as well as the Ca II K lines are polarised. These observational constraints are used to confirm or reject current theoretical models for the shaping mechanism
of the Red Rectangle. We propose that the observed polarisation is very unlikely generated by a uniform biconical stellar wind. Also, the hypothesis of a precessing jet does not completely match the observations since it will require a jet aperture larger than that of the nebula.