2 Arduino controller boards - 1 shared input
You don't need to add anymore components to your schematic. But you can leave some components.

Before you're adding a button to your schematic please consider first how you want to detect your signal. A logic 1 as if a button is pressed? Or logic 0 as if a button is pressed. You can do this using pull-up and pull-down resistors. These resistors should be wired like this.



(The 100Ohm resistor in an internal resistor from the MCU)

Using the pull-down resistor means that when the button is pressed you'd get a logic 1.
Using pull-up resistors means that when the button is pressed you'd get a logic 0.

When I see your schematic it seems like you're trying to make a pushbutton with pull-down resistor. Then you should wire your arduino like this.



Another option is to use the Arduino internal pull-up resistors. That way you don't have to add the 10k resistor in your schematic. And your schematic will look like this.



To use the internal pull-up resistors from the Arduino you'll need to put this in your setup(): pinMode(pin, INPUT_PULLUP); where pin should be your pin number. Please keep in mind that when you use the internal pull-up resistor a logic 0 means the button is pressed.