If you believe your departing will be in good terms, ask your HR. If not or if you are not sure how your departure will be received by the company, ask a lawyer.
In most cases, "written communication" simply means they want clear communication in no uncertain terms, that you have communicated your intended date of departure at a certain date, so the various people that have to then do the various red tapes know when you will leave and can prepare accordingly (payslips, employment record, reassigning work, hiring for replacements, removing access privileges, etc). They don't want this to be mentioned on the passing to your manager, who might then forget to pass the info to HR or pass it late, that they have to rush the red tapes. Email may suffice for this requirement, and in this case, the HR might not necessarily appreciate a physical copy which can be easily misplaced or searched, especially if they have to scan or retype it to let other people know of the details of your departure.
In other cases, "written communication" means they want to archive the physical copy with signature for legal/audit/archival/whatever purpose. In this case, you want to print this out and sign it with a pen and ask your HR what other details/attachments are necessary to be put into the physical copy and who has to countersign if any.
This may be described in your employment contract or in employee handbook, but if not, the only way to find out is ask your HR.
If you don't trust your employer though, if you think they might try make your departure difficult for whatever reasons, then you want to ask a lawyer how best to deliver your departure. Also, you want to ask for a receipt of any letters that you have delivered to them and anything they said. This kind of precaution may be necessary if you have reason to distrust your employer.