Should I include a pull-up resistor for this application? simple schematic
The second paragraph of the datasheet you linked says:


  These single channel devices are available with a complementary
  push−pull output in the NCS2250 or with an open drain output in the
  NCS2252.




Table 2 confirms that you don't need one for the 2250. The push-pull output can pull the output high or low without the need for a pull-up. The 2252 can only pull low so it does one. The open-drain type can be convenient when several can be wired in parallel to provide an OR function; any one of them pulling low pulls the output low.