The NHS need your consent to treat you. Your consent should be given voluntarily, if you do not wish to be treated and you sign a consent form, it means nothing. So the answer is no you do not have to sign the form. Here is an article on giving consent that talks about this is more detail: http://www.nhs.uk/Conditions/Consent-to-treatment/Pages/How-does-it-work.aspx
You have to be classed as capable of making an informed decision to refuse treatment. For people with mental health problems, there may be circumstances when their condition may be judges as affecting them to such a degree as to affect their capacity to make an informed choice. In these situations treatment can be given without consent. This is done under the mental health act And needs the agreement of two doctors and a mental health worker. It's also known as being sectioned, it can be challenged legally. This can only be used if there is evidence of risk of harm to self or others. Further information is available here: http://www.nhs.uk/Conditions/Consent-to-treatment/Pages/Capacity.aspx
In certain circumstances you can give an advance directive about what you will and won't consent to in the future, so that if you lack capacity then they refer back to your instructions given in the past. This means you can refuse treatment, however it does not apply to the mental health act.
I hope this gives you the information you need, please do reply with any further questions if you wish.
All the best,