  The magnetic structure of the antiferromagnetic square cupola compound
Ba(TiO)Cu$_4$(PO$_4$)$_4$ with the tetragonal structure is studied with 31P
nuclear magnetic resonance techniques. The magnetic hyperfine shift K shows a
clear splitting at the N\'eel temperature T$_N$ = 9.5 K, where the resonance
splits into two lines when an external magnetic field is oriented along the c
axis and into four lines when the field is along the a axis. In the
paramagnetic region K(T) follows temperature dependence of the magnetic
susceptibility $\chi(T)$. From K vs $\chi$ plot we determined nearly isotropic
hyperfine field values Ha_hf = 765 mT/$\mu_B$ and Hc_hf = 740 mT/$\mu_B$ for
the magnetic field oriented along a and c, respectively. From the rotation of
the single crystal in the external magnetic field we determined eight different
orientations of K-tensor in the paramagnetic region. In the antiferromagnetic
state at T = 6 K we found that the local field at phosphorus is mainly due to
dipolar field of coppers. Here the rotation of the single crystal shows eight
different orientations of the local field Bint = 35.6 mT. The orientations
correspond to the calculation of dipolar fields at phosphorus assuming magnetic
quadrupolar configuration of magnetic moments $\varGamma_3(1)$ described
previously [Nat. Commun. 7, 13039 (2016); Phys. Rev. B 96, 214436 (2017)].
