In this work, we investigate the complexation behavior of poly(oligo(ethylene glycol)methyl methacrylate)-co-poly(2-(diisopropylamino)ethyl methacrylate), P(OEGMA-co-DIPAEMA), hyperbranched polyelectrolyte copolymers, synthesized by reversible addition fragmentation chain transfer (RAFT) polymerization, with short-linear DNA molecules. The synthesized hyperbranched copolymers (HBC), having a different chemical composition, are prepared in order to study their ability to bind with a linear nucleic acid at various N/P ratios (amine over phosphate groups). Specifically, the three pH and thermo-responsive P(OEGMA-co-DIPAEMA) hyperbranched copolymers were able to form polyplexes with DNA, with dimensions in the nanoscale. Using several physicochemical methods, such as dynamic and electrophoretic light scattering (DLS, ELS), as well as fluorescence spectroscopy (FS), the complexation process and the properties of formed polyplexes were explored in response to physical and chemical stimuli such as temperature, pH, and ionic strength. The mass and the size of polyplexes are shown to be affected by the hydrophobicity of the copolymer utilized each time, as well as the N/P ratio. Additionally, the stability of polyplexes in the presence of serum proteins is found to be excellent. Finally, the multi-responsive hyperbranched copolymers were evaluated regarding their cytotoxicity via in vitro experiments on HEK 293 non-cancerous cell lines and found to be sufficiently non-toxic. Based on our results, these polyplexes could be useful candidates for gene delivery and related biomedical applications.