Sanity check with potential project. IoT with a dishwasher
If connecting to the wiring, using an opto-coupler will ensure that your Arduino's days will be long on the face of the land. If it is an LED indicator you may be able to connect the opto-coupler LED  input directly across the existing LED, but use of an appropriate series resistor would be wise. Optocoupler LEDs may have about 2 V forward operating voltage which is in the same range as a red LED. Some use lower forwards voltage LEDS (probably IR).  

If your opto coupler has low input current requirements then connecting it via a series resistor across the existing LED will allow the indicator to still operate. 

R series = (Vsource - V_opto_LED) / I_opto.
eg 12V source, 2V opto_LED (typical), 1 mA (should be enough for logiclevel signal.)
R = (12-2) / .001 A = 10/.001 = 10 k Ohm.

For direct connection across an existing red LED a 100 Ohm series resistor should avert disaster.
V drop in resistor at 1 mA:
V = IR = 0.001 x 100 = 0.1 V
= liable to be OK.

Ask if more information wanted.