Deuteronomy 22:5 in the KJV states:
"A woman must not wear men's clothing, and a man must not wear women's clothing. The LORD [Jehovah] your God detests people who do this."
What is Deuteronomy 22:5 Really Saying and Does This Still Apply to Christians Today?
When this law was given, both men and women wore robes. Yet there was a difference with the style of the robes. It is similar today. There are men's pants and there are women's pants.
The principle of the law at Deut. 22:5 was for a man to WANT to look like a man and for a woman to WANT to look like a woman. An example has been given that if a woman were to put on a worn-out pair of her husband’s trousers to do a job around the house she wouldn't be going against the evident purpose of the law, namely, to prevent confusion of sexual identity and sexual abuses.
But even though the law itself is no longer binding since it is from the Mosaic Law and Christians today are no longer under the Mosaic law, the same principle mentioned above still stands today.
Also see:
Dress (Deut. 22:5) Insight-1 pp. 652-656; Watchtower Online Library)
11/2/72 Watchtower, Questions from Readers
Mosaic Law - Links to Information (Search For Bible Truths)