In MA, I can just tell the RMV I lost the plate (online), and I get a form to keep in my car for a lost plate. I do it about twice a year, it's $10 per plate. The one time I got a ticket while parked, I emailed in the form and the ticket was dropped.
I looked in CT, and without a police report it looks to be $25.
https://portal.ct.gov/DMV/Registrati...License-Plates
In MA, it's like 6+ weeks until you get the replacement plate, but the form to keep in your car for missing a plate doesn't expire until your registration date (which can be many months away in most cases).
I also have my plate with carbonio mount in my trunk as a backup ("I took the car through a car wash and forgot to put back on?")