From the UC Transfer admission guide:
Colleges
• Before entering any coursework and grades, you’ll need to first enter information about all colleges/universities attended, including dates of attendance for each college, term system, and diploma or certificate information.
• Dates of attendance should be entered as consecutive dates even if enrollment was interrupted, (i.e if you took some time off and then went back to that school, you’ll
still need to enter the first month/year of attendance through the last month/year of attendance).
Here is a link for the UC transfer application guide. Nothing is mentioned that you need to indicate your “current” CC on the application unless this guide is not updated.