The rotational spectrum of NSF3 in the ground and v5 = 1 vibrational states has been investigated in the centimeter- and millimeter-wave ranges. R-branch (J + 1 <-- J) transitions for J = 0, 1 and Q-branch rotational transitions for the v5 = 1 vibrational state have been measured by waveguide Fourier transform microwave spectroscopy in the range 8-26.5 GHz. The Q-branch transitions include 28 direct l-type doubling transitions (kl = +1, A1) <--> (kl = +1, A2) with J < or = 62, and 108 direct l-type resonance transitions following the selection rule delta k = delta l = +/-2 with J < or = 60 and G = |k - l| < or = 3. A process called "regional resonance" was observed in which a cluster of levels interacted strongly over a large range in J. This process led to the observation of 55 perturbation-allowed transitions following the selection rules delta(k - l) = +/-3, +/-6. In particular, (kl = +1, A+) <--> (kl = -2, A-), (kl = +4, A+) <--> (kl = +1, A-), (kl = +2) <--> (kl = -1), (kl = +3) <--> (kl = 0), (kl = +2) <--> (kl = -3), and (kl = +3) <--> (kl = -3). The various aspects of the regional resonances are discussed in detail. An accidental near-degeneracy of the kl = 0 and kl = -4 levels at J = 26/27 led to the observation of perturbation-allowed transitions following the selection rule delta(k-l) = +/-6 with (kl = +2) <--> (kl = -4). A corresponding near-degeneracy between kl = -1 and kl = -3 levels at J = 30/31 led to the detection of similar transitions, but with (kl = +3) <--> (kl = -3). In the range 230-480 GHz, R-branch rotational transitions have been measured by absorption spectroscopy up to J = 49 in the ground-state and up to J = 50 in the v5 = 1 vibrational state. The transition frequencies have been analyzed using various reduced forms of the effective Hamiltonians. The data for the v5 = 1 vibrational state have been fitted successfully using two models up to seventh order with delta k = +/-3 interaction parameters constrained (dt constrained to zero, and epsilon to zero or to the ground-state value). On the other hand, reductions with the (delta k = +/-1, deltal = -/+2) interaction parameter q12 fixed to zero failed to reproduce the experimental data since the parameters defining the reduction transformation do not arise in the correct order of magnitude. The ground-state data have been analyzed including parameters up to fourth order constraining either parameters of the delta k = +/-3 interactions to zero (reduction A), or of the delta k = +/-6 interactions to zero (reduction B). The unitary equivalence of the different parameter sets obtained is demonstrated for both vibrational states.