We have obtained rotationally resolved pulsed field ionization-photoelectron (PFI-PE) spectra of CO in the energy range of 13.98-21.92 eV, covering the ionization transitions CO+(X (2)Sigma(+),v(+)=0-42,N+)<-- CO(X (1)Sigma(+),v"=0,N"). The PFI-PE bands for CO+ (X (2)Sigma(+), v(+)=8-22, 24, and 28-39) obtained here represent the first rotationally resolved spectroscopic data for these states. The high-resolution features observed in the PFI-PE spectra allow the identification of vibrational bands for the CO+ (X (2)Sigma(+), v(+)=10, 14, 15, 17, 18, 21, 24, 25, 29-31, 33, 35-37, and 39) states, which strongly overlap with prominent vibrational bands of the CO+(A (2)Pi(3/2,1/2),B (2)Sigma(+)) states. The simulation using the Buckingham-Orr-Sichel model has provided accurate molecular constants for CO+(X (2)Sigma(+),v(+)=0-42), including ionization energies, vibrational constants (omega(e)(+)=2218.8 +/- 3.5 cm(-1), omega(e)(+)x(e)(+)=16.20 +/- 0.32 cm(-1), omega(e)(+)y(e)(+)=0.074 +/- 0.011 cm(-1), and omega(e)(+)z(e)(+)=-0.001 83 +/- 0.000 13 cm(-1)), and rotational constants [B-e(+)=1.9797 +/- 0.0051 cm(-1), alpha(e)(+)=0.0201 +/- 0.0011 cm(-1), gamma(e)(+)=0.000 122 +/-0.000 067 cm(-1), z(e)(+)=-(5.2 +/- 1.1)x10(-6) cm(-1)]. Enhancement of Delta N < 0 rotational branches, attributable to field-induced rotational autoionization, was clearly discernible in PFI-PE bands for CO+ (X (2)Sigma(+), v(+)=0-5, 11, and 12). Significant local enhancements due to near-resonance autoionization were observed for low v(+) (< 10) PFI-PE bands of CO+(X (2)Sigma(+)), where the density of interloper Rydberg states converging to higher ionic levels is high as manifested in the photoion spectrum. The observation of a long vibrational progression in the Franck-Condon gap region, where strong autoionization states are absent, is consistent with the suggestion that high-n Rydberg states converging to highly excited vibrational levels of CO+(X (2)Sigma(+)) are partially populated via direct excitation to a repulsive neutral state. The relatively minor band intensity variation observed for high v(+) PFI-PE bands is also in accord with the direct excitation model. Since Delta N=0, +/- 1, +/- 2, and +/- 3 rotational branches are observed in the PFI-PE spectra, we conclude that the ejected photoelectrons are restricted to angular momentum continuum states l=0-4.