  Hadronic production of $P$-wave charmonium states $\chi_{cJ}$ in hadronic
interaction is considered. Using experimental results of CDF and LHCb
collaborations we show, that contributions of color-singlet components are
dominant. As for color-octet mechanism, we show, that contributions from
$P$-wave states can also be observed, while $S$-wave states can be neglected.
The best experimental observables that give information about relative
importance of color-singlet and color-octet components are the ratios
$\chi_{c2}/\chi_{c1}$ and $\chi_{c0}/\chi_{c1}$.
