The first pitch invasion followed Rochdale’s opener in the 96th minute with the club needing victory to top the table and gain automatic promotion.
The second invasion came after York’s dramatic equaliser in the 113th minute.
Police said four Rochdale fans were arrested following the incidents, one on suspicion of assault and pitch incursion, one on suspicion of a public order offence, and two on suspicion of pitch incursion.
One male York City fan was arrested on suspicion of assault, with police saying he would be interviewed at a later date.
The incidents are also under investigation by the Football Association.
Sport has approached York and Rochdale for comment.
York and Rochdale had amassed 212 points between them heading into the final-day showdown, with York needing to avoid defeat to secure a return to League Two.
