Can my boss refuse to pay me for overtime hours if I didn't take my time off?

Under the Canada Labour Code, you have a choice between receiving overtime pay or taking time off with pay. Since you and Sarah signed a written note, you have entered into a valid agreement for time off [cite:ca-labour-code-sec174]. According to the law, an employee is entitled to time off if "at their request, they and the employer enter into an agreement in writing providing for the taking of time off" [cite:ca-labour-code-sec174]. This means your signed note is a binding agreement regarding your 20 hours of overtime. Your agreement specifies that you will take this time during the first week of February. This is allowed because the law permits a longer period than the standard three months if there is a written agreement, provided that period does not exceed 12 months [cite:ca-labour-code-sec174]. If you do not actually take the time off by the date you and Sarah agreed upon, the company's policy cannot override your legal rights. The law states that "If the employee does not take all or part of the time off within the applicable period... the employer shall, within 30 days after the day on which that period ends, pay the employee’s wages for the overtime for which the time off was not taken" [cite:ca-labour-code-sec174]. This payment must be at a rate of "not less than one and one-half times the employee’s regular rate of wages" [cite:ca-labour-code-sec174]. In your case, if you take the time in February as planned, you get the time off. If for some reason you do not take it, Sarah's claim that the company won't pay you because you haven't used the hours yet is incorrect; the law requires them to pay you within 30 days after the agreed period ends.