How to record stock dividends on a tax return?

A stock dividend with no option of a cash payment is treated the same as a stock split. The number of shares you own changes, but you owe no tax on the stock dividend and the receipt of a stock dividend does not appear on the tax return.

When you go to sell stock for which you have received stock dividends, the cost per share is spread among all of the shares in determining your gain or loss on the sale.

In your example, say Michelle had 200 shares with a cost of $12/share, or a basis of $2400. She received a stock dividend of 40 shares. She now has 240 shares, but her basis is still $2400, and her cost per share is now $10/share.

Stock dividends are not taxable there was no money received or right to receive money. The basis in the new stock is an allocable portion of the stock previously held in the proportion of fair market value of the old and new stock.

dividends are reported on 1099 D

Yes, and you will get a 1099 from the company.