We characterize the instability of an rf clock signal caused by free-space transmission of a frequency comb (FC) under typical laboratory conditions. The phase-noise spectra show the involvement of multiple random processes. For a 10 m transmission, the rms timing jitter integrated over 1-10(5) Hz is 95 fs, and the root Allan variance over 1 s is 4x10(-13). The measured Allan variance has a tau(-1) behavior and an excellent agreement with the phase noise measurement. These results indicate the feasibility of FC-based free-space rf clock distribution over short distances.