...Then again, I see that you actually have my @common_array;. If that's what you want to set, ignore objects and classes. That variable has nothing to do with either.
If all the code is in the same file, you can simply do @common_array = qw(1 2); since you are still in the same lexical scope.
If the definition (my @common_array;) and the code from which you want to access @common_array are in separate files, then you can't access the array from that code since the array is outside of the scope of the code in question.
You could work around that problem by using a package variable (our @common_array;) instead of a lexical variable (my @common_array;). Package variables are globally scoped (if you use their full name), which means you can access the array as @CommonObject::common_array from anywhere.