MIC6270 comparator - input voltage higher than supply rail
In addition to note 6, note 4 of the "Electrical characteristics" shown in the datasheet also explicitly states:


  The input common-mode voltage, VIN+, or VIN–
  must not go below –0.3V.  The upper end of the common-mode voltage
  range is V+ – 1.5V at 25°C, but either or both inputs can go to +36Vdc
  without damage, independent of VV+.


Therefore, if the inputs are within 36V, there won't be damage, but the common mode range must be within V+-1.5V, otherwise the part might not work correctly. 

In your case, if I understood correctly, you want to power it with 3V, and put one input to 18V. Regardless the other input, the common-mode voltage will be larger or equal to 9V, therefore it will exceed 3V - 1.5V = 1.5V. Therefore your solution might not work. Use a resistor divider if possible, to bring the VCM within the specified range. 

EDIT: (following what @berry120 got from Microchip as an answer).

Despite note 4, Microchip answered that it's enough that at least one of the two inputs is within the common mode voltage range.

In fact, here's what Microchip replied:


  Most comparators (this device included) only require that one input
  remains in common mode range for it to function properly. As long as
  one input is in the common range mode, the other input can accept a
  voltage greater than Vcc. If you power the device with 3V, you must
  ensure that one of the inputs does not go over 1V or below -0.3V for
  the whole temperature range.


Still, if your signal goes from 0V to 18V, then comparing that signal (or better, its divided version) with 0 will lead to unpredictable results due to offsets. To check if 18V is above a certain value, compare it to a value larger than 0 (e.g. 0.5V or so), so that, when the input voltage goes to 0, the comparator will compare 0.5 to 0, and not 0 to 0 (plus offsets).



By the way, is not so uncommon that in some IC you can feed a voltage higher than the supply: think about a 5-V tolerant IC, powered at 3.3V.

In addition, on some ICs, you can also safely tie an open drain/collector output above Vcc/Vdd. For instance the output of comparator LM311 can be tied up to 40V (abs maximum rating), even if you power it at 5V.