The petticoat with the microcontroller, battery and all of the LEDs sits underneath the dress and can't be accessed without pulling up the dress or putting the microcontroller at the bottom making it hard to reach. In addition, the color sensor needs to be in a central place on top of the dress.
The solution to connecting it all together - snaps! Or to be precise conductive snaps.
The idea is to snap the petticoat to the dress, then snap on another element on top of the dress (the belt) to hold the color sensor and then run conductive thread from one set of snaps to the other. This will also enable detaching the belt and the petticoat and connecting them to another dress/skirt.
Finally there is an on/off reset snap on the dress that runs all the way down to the battery.