What this question is really asking is whether or not Newton's laws apply to accelerating reference frames, also called non-inertial reference frames.
What are some examples of accelerating reference frames? Well a common one would be your car. Imagine yourself sitting in the passenger seat of a car (yes, the passenger seat. Let your friend do the driving, you're busy doing physics!). From your point a view you are sitting still relative to the rest of the car, even though the car may be speeding up, slowing down, or going around a curve (all instances where the car is accelerating).
Now, imagine you place a book on top the dashboard in front of you. If your friend slams on the gas and rapidly accelerates the car, what will happen to the book? You'd expect it to slide backwards and fall on your lap. You could also imagine placing a bag of groceries on the back seat. Your friend slams on the breaks and the bag will fly forward. In each case there was no force acting on the object and yet it appeared to move. Now recall what was Newton's first law?
An object at rest tends to stay at rest and an object in motion tends to stay in motion unless acting upon by an external force.
From your point of view (passenger in the car), the book and bag of groceries were at rest. Yet, when the reference frame accelerated the objects appeared to move without any external forces acting on them. This violates Newton's first law. Therefore, the answer to the original question is TRUE, Newton's laws apply only to reference frames that are not accelerating.
In many instances when we are dealing with accelerating reference frames, we will introduce so called 'fictitious forces' to account for this sort of behavior. These would be forces like centrifugal force or Coriolis forces (both having to do with rotating reference frames). If we include these 'fictitious forces' then we can still apply Newton's laws to non-inertial reference frames.