In contrast to the predictions of the unified model, some X-ray unobscured Seyfert 2 galaxies have been discovered in the last decade. One of them, the starburst/Seyfert composite galaxy IRAS 01072+4954 (z = 0.0236), has a typical Type-1 X-ray emission, while its optical spectrum resembles an H ii galaxy and lacks the expected broad lines. We performed near-infrared integral-field observations of this object with the aim to determine the nature of its nuclear emission and to find indications for the existence or absence of a broad-line region. Several reasons have been proposed to explain this peculiar emission. We studied the validity of these hypotheses, including the possibility for this galaxy to be a True-Seyfert 2. We found little obscuration toward the nucleus A V = 2.5 mag, and a nuclear star-formation rate Σ SFR < 11.6 M yr −1 kpc −2 , which is below the average in Seyferts. Unresolved hot-dust emission with T ∼ 1150 K seems to indicate the presence of a torus with its axis close to the line of sight. We found that IRAS 01072+4954 hosts a low-mass black hole with an estimated mass of M BH ∼ 10 5 M . Its bolometric luminosity is L bol 2.5 × 10 42 erg s −1 , which yields a high accretion rate with an Eddington ratio λ Edd 0.2. If the relations found in more massive systems also apply to this case, then IRAS 01072+4954 should show broad emission lines with a FWHM broad ∼ (400−600) km s −1 . Indeed, some indications for such narrow broad-line components are seen in our data, but the evidence is not yet conclusive. This source therefore does not seem to be a True-Seyfert 2, but an extreme case of a narrow-line Seyfert 1, which, due to the faintness of the active nucleus, does not have strong Fe ii emission in the optical.