To give a managed identity access to an Azure resource, you need to add a role to the target resource for that identity.
Note: To easily authenticate access to other resources that are protected by Azure Active Directory (Azure AD) without having to sign in and provide credentials or secrets, your logic app can use a managed identity (formerly known as Managed Service Identity or MSI). Azure manages this identity for you and helps secure your credentials because you don't have to provide or rotate secrets.
If you set up your logic app to use the system-assigned identity or a manually created, user- assigned identity, the function in your logic app can also use that same identity for authentication.
Reference:
https://docs.microsoft.com/en-us/azure/logic-apps/create-managed-service-identity
https://docs.microsoft.com/en-us/azure/api-management/api-management-howto-mutual-certificates-for-clients