You are not required to sign a warning letter and you should certainly not do so if you consider the warning to be unjust or unreasonable.
However, given that the letter will form part of your employee record, you should seek an immediate explanation from your employer and address your concerns about the written warning.
Under section 387 (c) of the Fair Work Act (FWA) 2009 (Cth) an employee must be given the opportunity to respond to any warnings related to their conduct or capacity.
A warning letter is unfair if it is vague about the reasons for the warning and does not provide any direction as to how you should remedy the situation. Importantly, you should be given a reasonable amount of time to improve your alleged unsatisfactory conduct.
If you believe that the warning is unfair, you should give a clear and detailed explanation why. It is recommended that you write a letter disputing the basis of the warning and include your version of the specific events and if possible highlight that your conduct was in keeping with company policy.
You should also review your employee handbook for any possible dispute resolution procedures and give your letter of dispute to your immediate supervisor and/or HR Manager.
If you have received a warning letter which you view to be unfair and your employment is terminated, you may have grounds to make an unfair dismissal claim with the Fair Work Commission. Given there is a 21-day time limit within which you can bring a claim against your former employer, you should seek legal advice immediately.