Yes, you can.
Follow these steps to download a statement:
1. Open the Countingup app, and tap the "get statement" icon underneath your available balance on the 'Balance' tab
2. Select the date period you want a statement for
3. Ensure the ‘Printable’ toggle is on to get a PDF statement, and the Raw data toggle is on to get a CSV statement
4. Tap 'Send statement'