Three supernova remnants (SNRs) form the CTB 37 complex: CTB 37A (G348.5+0.1, associated with the TeV γ-ray source HESS J1714−385), CTB 37B (G348.7+0.3, associated with HESS J1713−381 and the magnetar CXOU J171405.7.381031) and G348.5−0.0. We use 21-cm H i absorption measurements to constrain kinematic distances to these SNRs, which have not previously been determined well. We revise the kinematic distance for CTB 37A to be in the range 6.3–9.5 kpc (previously ∼11.3 kpc) because it is beyond the near 3-kpc arm and in front of the far side of the CO cloud at −145 km s−1 towards l= 348.5. G348.5−0.0 has an H i column density (∼6.1×1021 cm−2) lower than CTB 37A (∼7.1 × 1021 cm−2). Also, G348.5−0.0 does not have the major absorption feature at −107 km s−1 that CTB 37A shows. This is caused by the near 3-kpc arm, so G348.5−0.0 is at a distance of ≤6.3 kpc. CTB 37B is at a distance of ∼13.2 kpc (previously 5–9 kpc) based on: (1) it has an absorption feature at −10 ± 5 km s−1 from the far 3-kpc arm, so CTB 37B is behind it; (2) there is absorption at −30 km s−1 but not at −26 km s−1, which yields the distance value; and (3) the H i column density towards CTB 37B (∼8.3 × 1021 cm−2) is larger than that towards CTB 37A. In summary, CTB 37A, CTB 37B and G348.5+0.0 are all at different distances and are only by chance nearby each other on the sky. In addition, we conclude that CTB 37A and 37B are not associated with the historical supernova AD 393.