No, there is no need for witnesses--the concept of "due process" does not apply to an employer's internal discipline or termination decisions, so you could be written up, disciplined, demoted,  suspended, or even fired without any proof, unless:1) You have an employment contract (or union agreement) which requires evidence, specifies a process to be followed in cases like this, or limits the grounds for which action could be taken against you;2) Your negative treatment is actually based on discrimination against you for a protected characteristic, such as race, religion, sex, age over 40, or disability; or3) Your negative treatment is retaliation for having filed  a protected claim, such as a wage and hour claim, a discrimination claim, or for FMLA leave.