  We analyze all of the available {\it RXTE} observations of Cyg X-3 in order
to investigate the connection between the central X-ray source and its
surrounding environment. The hardness--intensity diagram of Cyg X-3 displays a
"shoe" shape rather than the Q-type shape commonly seen in other black hole
X-ray binary, and exhibits no apparent hysteresis effect. During the
$\gamma$-ray outbursts, no existing data are located in the hard and
intermediate states, which suggest the absence of a significant population of
non-thermal electrons when the source is in these states. For the first time,
we present the orbital modulation of the X-ray light curve (LC) of all five
states. The different energy band LCs are in phase with each other in all five
states, and the modulation amplitude of both soft and hard X-ray LCs
monotonously increases with decreasing hardness from hard to soft non-thermal
states. We confirm that the modulation depth decreases with increasing energy
in the hard, intermediate, and very high states, as originally reported by
Zdziarski et al. However, in the soft non-thermal state, the hard X-ray
modulation strength significantly increases and is even larger than the soft
X-ray one. Our results rule out both wind absorption and jet origins of the
hard X-ray LC modulation in the soft non-thermal state, and challenge our
understanding of the states of Cyg X-3.
