code: void connectAndRequestGoogleAccount(int signInRequestCode, int errorResolutionRequestCode) {
          if (client.isConnected()) {
              requestGoogleAccount(signInRequestCode);
          } else if (!client.isConnecting()) {
              this.signInRequestCode = signInRequestCode;
              this.errorResolutionRequestCode = errorResolutionRequestCode;
              client.connect();
          }
      }
docs: Checks if the Google API Client is connected and tries to request the user Account.
  
  @param signInRequestCode          the request code to use when you expect the sign in result.
  @param errorResolutionRequestCode the request code to use when you expect the erorr resolution result.