The differential cross sections of the $^{12}$C($^3$He,t)$^{12}$N reaction leading to formation of the 1$^+$ (ground state), 2$^+$(0.96 MeV), 2$^{-}$(1.19 MeV), and 1$^{-}$(1.80 MeV) states of $^{12}$N are measured at $E$($^3$He)=40 MeV. The analysis of the data is carried out within the modified diffraction model (MDM) and distorted wave Born approximation (DWBA). Enhanced $rms$ radii were obtained for the ground, 2$^{-}$(1.19 MeV), and 1$^{-}$(1.80 MeV) states. We revealed that $^{12}$B, $^{12}$N, and $^{12}$C in the IAS with T=1, and spin-parities 2$^{-}$ and 1$^{-}$ have increased radii and exhibit properties of neutron and proton halo states.
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