Azure Logic Apps - Authenticate with managed identity for Azure AD OAuth-based connectors

I managed to get this working using managed identity, all you need to do is to pass the following in the API connection 

"type": "Microsoft.Web/connections",
"properties": {

  "parameterValueType": "Alternative"

You might still need to assign a role to the identity in the resource you are trying to access using the identity

But as mentioned above, you can use service principle and pass their details in the API connection

"type": "Microsoft.Web/connections",
"properties": {

  "parameterValues": {
    "token:TenantId": "[subscription().tenantId]",
    "token:clientId": "[parameters('servicePrincipleId')]",
    "token:grantType": "client_credentials",
    "token:clientSecret": "[parameters('servicePrincipleSecret')]"

Service principle needs to have the role assigned too