Breathing crystals based on polymer-chain complexes of Cu(hfac)(2) with nitroxides exhibit thermally and light-induced magnetostructural anomalies in many aspects similar to a spin crossover. In the present work, we report the synthesis and investigation of a new family of Cu(hfac)(2) complexes with tert-butylpyrazolylnitroxides and their nonradical structural analogues. The complexes with paramagnetic ligands clearly exhibit structural rearrangements in the copper(II) coordination units and accompanying magnetic phenomena characteristic for breathing crystals. Contrary to that, their structural analogues with diamagnetic ligands do not undergo rearrangements in the copper(II) coordination environments. This confirms experimentally the crucial role of paramagnetic ligands and exchange interactions between them and copper(II) ions for the origin of magnetostructural anomalies in this family of molecular magnets.