Hi Susan,
Customer and Billing Cycle reports store a 'Last Stmt Date' (last statement date) value, which you could see by including this field on the Edit Customer or Edit Billing Cycle grids with the column editor. It is this that gets updated when printing statements, and has no effect on clearing completed transactions to history if you choose to do this by Period End.
Another effect of this question is that if you have the company profile option to add a Note to the customer when statements are printed (or emailed or faxed), then choosing Yes will add the note, and No will not add the note.
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Regards,
Softrak Tech Support