Legal Question in Employment Law in California

They 'can' do anything they like. Using such write up later in discipline or termination would only raise issues of 'notice'. But....

Employees have the 'right' to pay and employee benefits per the minimum wage laws, and company policy as agreed, to be provided a 'safe' workplace to minimize risk of injury, and sometimes are entitled to certain medical/pregnancy leave rights. That's about it. In general, unless an employee is civil service, in a union, or has a written employment contract, they are an 'at will' employee that can be disciplined or fired any time for any reason, with or without �cause�, explanation or notice, other than for illegal discrimination, harassment or retaliation under the ADA disability, Civil Rights [age, race, sex, ethnic, religion, pregnancy, etc], Whistle-blower, or similar statutes. The employee's goal should be to keep the employer happy.