No.
This is automatically calculated based on the “medical cost details” received by the Health Insurance Society from the medical institution, and, if the copayment amount exceeds 20,000 yen (based on the total High-Cost Medical Care Benefits and additional benefits), we pay the excess amount.
The calculation method differs depending on the medical institution (and department), the month, and whether the treatment is inpatient or outpatient. Note that this only applies to costs covered by insurance, not the cost of meals, the private room charges incurred during hospitalization, or other things you are responsible for paying for.
Payments are generally made by the end of the month three months after the treatment is received. After completing the procedure, a notice will be sent to your house.

Note that, if you use a Myna health insurance card, your payment at the service counter will not exceed the cost-sharing maximum amount. (It is not necessary to present a Certificate of Application of Maximum Copayment Amount.)。