To search for low-energy resonant structures in isospin T=3/2 three-body systems, we have performed the experiments ^{3}H(t,^{3}He)3n and ^{3}He(^{3}He,t)3p at intermediate energies. For the 3n experiment, we have newly developed a thick Ti-^{3}H target that has the largest tritium thickness among targets of this type ever made. The 3n experiment for the first time covered the momentum-transfer region as low as 15 MeV/c, which provides ideal conditions for producing fragile systems. However, in the excitation-energy spectra we obtained, we did not observe any distinct peak structures. This is in sharp contrast to tetraneutron spectra. The distributions of the 3n and 3p spectra are found to be similar, except for the displacement in energy due to Coulomb repulsion. Comparisons with theoretical calculations suggest that three-body correlations exist in the 3n and 3p systems, although not enough to produce a resonant peak.