You can have multiple locals for the same control, but you need to be very careful about creating race conditions. If the update of the local is done only at specific points in time in response to user interaction, then you should usually be fine. Assuming you use an event structure to process the UI events from the control, you can usually update the control with safety in other cases of that event structure (in response to the other things the user does in the UI).
I should note that I'm assuming that you're only using the control as a UI control, not as a variable. I know that NI gave them the name local variables and that they work similarly to variables in other languages, but generally, you should not use controls and indicators as variables. It works, but you run the risk of race conditions. Instead, you use wires to move the data from function to function.
What I described in the first paragraph is only one way of doing things. Often, if you have a more complex piece of code it's usually better to keep the actual current values not in the UI, but in a separate place where you can always make sure they are all synchronized (such as a cluster of state data in a shift register). Then you ignore the value in the control and only update from it when it is changed by the user.
There's quite a lot of material around, but I suggest you start by looking at some of these tutorials.
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