We present Yebes 40m telescope observations of the three most stable C4H3N isomers towards the cyanopolyyne peak of TMC-1. We have detected 13 transitions from CH3C3N (A and E species), 16 lines from CH2CCHCN, and 27 lines (a-type and b-type) from HCCCH2CN. We thus provide a robust confirmation of the detection of HCCCH2CN and CH2CCHCN in space. We have constructed rotational diagrams for the three species, and obtained rotational temperatures between 4-8 K and similar column densities for the three isomers, in the range (1.5-3)×1012 cm-2. Our chemical model provides abundances of the order of the observed ones, although it overestimates the abundance of CH3CCCN and underestimates that of HCCCH2CN. The similarity of the observed abundances of the three isomers suggests a common origin, most probably involving reactions of the radical CN with the unsaturated hydrocarbons methyl acetylene and allene. Studies of reaction kinetics at low temperature and further observations of these molecules in different astronomical sources are needed to draw a clear picture of the chemistry of C4H3N isomers in space.