Context. The interstellar detections of isocyanic acid (HNCO), methyl isocyanate (CH 3 NCO), and very recently also ethyl isocyanate (C 2 H 5 NCO), open the question of the possible detection of vinyl isocyanate (C 2 H 3 NCO) in the interstellar medium. There are only low-frequency spectroscopic data (< 40 GHz) available for this species in the literature. This makes predictions at higher frequencies rather uncertain hampering its search in space by millimeter wave astronomy. Aims. The aim of the present study is, on one hand, to extend the laboratory rotational spectrum of vinyl isocyanate into the millimeter wave region and, on the other hand, to undertake a first check for its presence in the high-mass star forming region Sgr B2, where other isocyanates and a plethora of complex organic molecules are observed. Methods. The pure rotational spectrum of vinyl isocyanate was recorded in the frequency regions 127.5-218 and 285-330 GHz using the Prague millimeter wave spectrometer. The spectral analysis was supported by high-level quantum-chemical calculations. On the astronomy side, we assumed local thermodynamic equilibrium to compute synthetic spectra of vinyl isocyanate and to search for it in the ReMoCA survey performed with the Atacama Large Millimeter/submillimeter Array (ALMA) toward the high-mass star forming protocluster Sgr B2(N). Additionally, we searched for the related molecule ethyl isocyanate in the same source.Results. Accurate values for the rotational and centrifugal distortion constants are reported for the ground vibrational states of trans and cis vinyl isocyanate from the analysis of more than 1000 transitions. We report nondetections of vinyl and ethyl isocyanate toward the main hot core of Sgr B2(N). We find that vinyl and ethyl isocyanate are at least 11 and 3 times less abundant than methyl isocyanate in this source, respectively. Conclusions. Although the precise formation mechanism of interstellar methyl isocyanate itself remains uncertain, we infer from existing astrochemical models that our observational upper limit for the CH 3 NCO:C 2 H 5 NCO ratio in Sgr B2(N) is consistent with ethyl isocyanate being formed on dust grains via the abstraction or photodissociation of an H atom from methyl isocyanate, followed by the addition of a methyl radical. The dominance of such a process for ethyl isocyanate production, combined with the absence of an analogous mechanism for vinyl isocyanate, would indicate that the ratio C 2 H 3 NCO:C 2 H 5 NCO should be rather less than unity. Even though vinyl isocyanate was not detected toward Sgr B2(N), results of this work represent a significant improvement on previous low-frequency studies and will allow the astronomical community to continue in searching for this species in the universe.