For starters, as Solar Mike mentions, to some extent it should depend on your accelerometer and what it is capable of. That said, it's important to understand what you are measuring, and how that effects your question.
Acceleration is the change in velocity over time. This means that whether or not the object has negative or positive acceleration wont just depend on if it has a positive or negative velocity.
Picture an object moving in the $+x$ direction. Now imagine that an acceleration acts on the object that is decreasing it's velocity, while still moving in the $+x$ direction. The velocity is still moving in the $+x$ direction; but the acceleration is acting in the $-x$ direction; which causes an increase in negative velocity (or equivalently a decrease in positive velocity).
Basically, your accelerometer will not tell you directly which direction it is moving just based on the acceleration it is experiencing. You would need other information about starting conditions at least, to determine what your current velocity is given accelerations and times.
The accelerometer can tell you if the object is starting to gain or lose velocity in any direction; but acceleration alone cannot tell you what the current velocity is; unless you know initial velocity and account for all the accelerations leading up to the time you want to know about.