Add a role to an AWS Cognito Identity Pool via Cloudformation

I am trying to write a CloudFormation template to create a new Cognito identity pool with Google authentication and using a pre-existing role.

This code creates a new identity pool with google authentication -

Resources:
 cognitoid:
  Type: "AWS::Cognito::IdentityPool"
  Properties:
   "AllowUnauthenticatedIdentities": false
   "SupportedLoginProviders": { "accounts.google.com": "<Google client id>" }

For the role, AWS::Cognito::IdentityPool doesnt have anything in properties for attaching a role.