Yes, you can.
Follow these steps to download a statement:
1. Open the Countingup app, and tap the icon to the far right of your available balance on the 'Banking' 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'