In AmE, that piece of paper has a very non-technical sounding name - we simply call it a "doctor's note."
"You won't be paid for your absence unless you bring in a doctor's note."
"I swear I really was sick, Boss - here's my doctor's note."
Doctor: "Here's a prescription for an antibiotic, and I want you to stay home and rest for at least 48 hours."
Patient: "OK, but can you please give me a doctor's note that I can give to my boss?"
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