Both $\mathrm{PrBa}{\mathrm{Mn}}_2{O}_6$ and $\mathrm{NdBa}{\mathrm{Mn}}_2{O}_6$ have a structural transition coupled to an electronic localization and an antiferromagnetic transition. In both cases, the x-ray diffraction patterns reveal that the low-temperature phase is orthorhombic with lattice parameters $a+b,b-a$, and $c$ with respect to the tetragonal phase. Two possible solutions belonging to the space groups Pmam and $P{2}_{1}am$ can yield accurate refinements of the x-ray patterns. However, the active modes in the low-temperature phase disclosed by the Raman spectroscopy clearly point to the noncentrosymmetric space group, $P{2}_{1}am$. The symmetry analysis of this transition unveils that the primary modes belong to the irreducible representations M5− and GM5− and the main distortions correspond to rotations of the $\mathrm{Mn}{O}_6$ octahedra and an asymmetric combination of stretching and scissoring modes of the basal oxygens in these octahedra. We conclude that the low-temperature phase is polar and the main contribution comes from the displacement of oxygen atoms from their centrosymmetric positions. However, negligible contribution from the asymmetric stretching associated with a Jahn-Teller distortion is found in this structural transition, suggesting the lack of ferroic orbital ordering of $e_g$ ($3d_{x^2-y^2}$) orbitals in the orthorhombic $ab$ plane. There is only one inequivalent site for the Mn atom in the low-temperature polar phase so charge ordering cannot account for the electronic localization having a structural origin.