Currently, new functional materials are being created with a strong emphasis on their ecological aspect. Materials and devices based on DNA biopolymers, being environmentally friendly, are therefore very interesting from the point of view of applications. In this paper, we present the results of research on complexes in the powder form based on plasmid DNA (pDNA) and three surfactants with aliphatic chains containing 16 carbon atoms (cetyltrimethylammonium chloride, benzyldimethylhexadecylammonium chloride and hexadecylpyridinium chloride). The X-ray diffraction results indicate a local hexagonal packing of DNA helices in plasmid DNA complexes, resembling the packing for corresponding complexes based on linear DNA. Based on the Fourier-transform infrared spectroscopy results, the DNA conformation in all three complexes was determined as predominantly of A-type. The two relaxation processes revealed by dielectric spectroscopy for all the studied complexes are connected with two different contributions to total conductivity (crystallite part and grain boundaries). The crystallite part (grain interior) was interpreted as an oscillation of the polar surfactant head groups and is dependent on the conformation of the surfactant chain. The influence of the DNA type on the properties of the complexes is discussed, taking into account our previous results for complexes based on linear DNA. We showed that the type of DNA has an impact on the properties of the complexes, which has not been demonstrated so far. It was also found that the layer of pDNA-surfactant complexes can be used as a layer with variable specific electric conductivity by selecting the frequency, which is interesting from an application point of view.