Should I report the income that I got for short term return on investment(selling shares which I held less than 1 year) for state tax too?

I am reporting for FED. Not sure if I have to pay taxes for State too? I am resident of Alabama.

Yes, you do report the gain from sales of investments to AL - you report it on Schedule D and carry to Form 40 as "Other Income" on page 2, Part 1, line 3 - "Gain (or loss) from sale of Real Estate, Stocks, Bonds, etc."

Thank you.