The serial number is located on the main frame of your Catrike. The main frame is the largest diameter part of the frame and serial numbers are located towards the back of the Catrike behind/below the seat.
The serial number on newer Catrikes is engraved into the frame, so, it is permanent and cannot be removed. On newer Catrikes the serial numbers are preceded by the Catrike logo and they are a 5 digit number like 25555. You might need to look closely as the serial numbers are engraved prior to powder coating/painting.
On older generation Catrikes, the serial number was on a white adhesive backed label with black lettering. Older serial numbers begin with 3 letters followed by numbers like CTE1234.
See photos showing location of serial number on Catrikes in the owners manual. Find owners manual here.