  We investigate the differences in the stellar population properties, the
structure, and the environment between massive compact star-forming galaxies
(cSFGs) with or without active galactic nucleus (AGN) at $2<z<3$ in the five
3D-HST/CANDELS fields. In a sample of 221 massive cSFGs, we constitute the most
complete AGN census so far, identifying 66 AGNs by the X-ray detection, the
mid-infrared color criterion, and/or the SED fitting, while the rest (155) are
non-AGNs. Further dividing these cSFGs into two redshift bins, i.e., $2<z<2.5$
and $2.5 \leq z<3$, we find that in each redshift bin the cSFGs with AGNs have
similar distributions of the stellar mass, the specific star formation rate,
and the ratio of $L_{\rm IR}$ to $L_{\rm UV}$ to those without AGNs. After
having performed a two-dimensional surface brightness modeling for those cSFGs
with X-ray-detected AGNs (37) to correct for the influence of the central
point-like X-ray AGN on measuring the structural parameters of its host galaxy,
we find that in each redshift bin the cSFGs with AGNs have comparable
distributions of all concerned structural parameters, i.e., the Sersic index,
the 20\%-light radius, the Gini coefficient, and the concentration index, to
those without AGNs. With a gradual consumption of available gas and dust, the
structure of cSFGs, indicated by the above structural parameters, seem to be
slightly more concentrated with decreasing redshift. At $2<z<3$, the similar
environment between cSFGs with and without AGNs suggests that their AGN
activities are potentially triggered by internal secular processes, such as
gravitational instabilities or/and dynamical friction.
