Give some stream of consciousness and then the answer. On May 6, 2015, Fox cancelled the series after three seasons. On May 15, 2015 Hulu picked up the show, commissioning a 26 episode fourth season. On May 4, 2016, Hulu announced it had picked up the series for a 16-episode season 5, which was later reduced to 14. On March 29, 2017, Kaling announced the series would return for a sixth and final season; the final episode of the series aired on November 14, 2017.

Based on this passage, when did the mindy project move to hulu?
To answer this question, we should know that: On May 15, 2015 Hulu picked up the show, commissioning a 26 episode fourth season.
Therefore, the answer is May 15 , 2015.