Cell-free network architecture plays a promising role in the terahertz (THz) networks since it provides better link reliability and uniformly good services for all the users compared to the co-located massive MIMO counterpart, and the spatial-spectral THz link has the advantages of lower initial access latency and fast beam operations. To this end, this work studies cell-free spatial-spectral THz networks with leaky-wave antennas, to exploit the benefits of leveraging both cell-free and spatial-spectral THz technologies. By addressing the coupling effects between propagation angles and frequencies, we propose novel frequency-dependent THz transmit antenna selection schemes to maximize the transmission rate. Numerical results confirm that the proposed antenna selection schemes can achieve much larger transmission rate than the maximal ratio transmission of using all the transmit antennas with equal subchannel bandwidth allocation in higher THz frequencies.