As the previous poster said, a written record of a verbal warning is good practice.
In the past where I asked people sign documents say end of year reviews, etc... it was to acknowledge that they had received them. In the case that they wouldn't, put a note in explaining that the employee was present, the document explained to the employee and would ask another manager to sign it that it had been delivered. This was done in the presence of the employee, put a copy in their record and gave them a copy.
Means that if there are questions in the future that an employee can not say, I don't remember that or I didn't realise it was a warning, etc...
On the other side, if an employee wanted to go away and think about something that was fine. The could write anything they wanted it in as far as I was concerned - actually encouraged if they had comments that we put them in and addressed them. So if an employee wanted to put in why they felt it was unfair, or they had not been given sufficient time for improvement, etc... that was fine, it gave us something constructive to work with.
But once we were at the stage of a warning, I document all conversations - regardless of whether manager or employee. Actually I document most formal conversations/meetings just for clarification. Most just an email back to the individual sumarising what was agreed.