Determining if the length of LinkedList is even or odd
The method signature is a bit odd, returning a Boolean object instead of a primitive boolean.  A clearer name would be isListLengthEven().  The function could be static, since it does not rely on any object state.

If the list has one node, then your code will crash on if(head.next.next == null).  In general, you should avoid cluttering your code with unnecessary special cases.

You don't need to keep track of count.  This solution, like yours, is O(n), but it is much simpler:

public static boolean isListLengthEven(ListNode head) {
    for (; head != null; head = head.next.next) {
        if (head.next == null) return false;
    }
    return true;
}


The trick is to observe the loop invariant: each iteration through the loop, it advances head by two nodes, so that the picture at the top of the loop is always equivalent to the original.  If it can't advance by two, then the list has an odd length.