She sneaks in through the vents

Rouge had spent a long time looking over the buildings plans and realized that the vents had vulnerabilities she could exploit. Rouge glides over to the roof of the casino pulling out a pocket computer, she runs a hacking program that she persuaded Tails to give her.

"He's so adorable at times. Just a bit of flirting and he's willing to share all his toys. Maybe I should take him with me on my next vacation as thanks."

She uses the program to hack into the building's security and disables the vent sensors. Removing the vent cover she slips in. Rouge had freshly oiled up her slick outfit and this allowed her to navigate the tight spaces with ease as she moves to the lower levels. After the last time the owner is keeping the Chaos Emerald in the buildings less accessible lower levels. Unfortunately the building plans are fuzzy on what exactly is down there. But a little set back like that isn't enough to deter a master thief.

Rouge chuckles to herself. "Besides, not knowing exactly how it'll turn out is what makes this fun. This looks like a good spot to drop in."

Rouge opens a vent and enters the casino lower levels.