Yes, you may need to file a Gift Tax return, form 709 according to the IRS instructions concerning 709. Since there is no such thing as a joint gift tax return, each you and your wife may file a separate Gift Tax Return, each declaring $20,000 as the gift given to your son.
Since there is a $15,000 Income Exclusion, this means that you will each paying gift income of $5000 apiece. Please look over the instruction link given above for further details.
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