If Lucia constructed \( \overline{CD} \) as a copy of \( \overline{AB} \), then by definition of copying a segment using a straightedge and compass, she has created a segment \( \overline{CD} \) that is exactly the same length as \( \overline{AB} \).
Therefore, the correct statement is:
\[ AB = CD \]
So, the answer is:
AB = CD.