Labor's Ged Kearney celebrates her federal byelection win with Bill Shorten. Credit:AAP

Catholic education chiefs in Melbourne face the prospect of multiple investigations over their controversial intervention in last month’s Batman byelection on behalf of the ALP.

The Australian Greens party has confirmed it will lodge complaints with both the Australian Catholic Bishops Conference and the Australian Electoral Commission over robocalls and letters to Batman voters endorsing Labor’s education policies.

Well-placed sources also say an inquiry by the charities regulator, the Australian Charities and Not-for-profits Commission is likely given that, as a tax-exempt charity, Catholic Education Melbourne is not supposed to encourage voters to support one political party or candidate over another.

Catholic campaigning helped Labor retain its one-time safe seat in Melbourne’s inner north although electoral pundits doubt that the support was pivotal. The Liberals did not contest the byelection.