How do I apply limited income credit for my MA state tax. Turbo tax is not applying it even though my income of 12K per year qualifies for it.

Per Expert @John11_2 W152:

"It could be that you qualify for No Tax Status, which means that you wouldn't qualify for the LIC.  If your Massachusetts adjusted gross income was

• $8,000 or less if you're single
• $14,400 or less plus $1,000 per dependent if you're claiming head of household, or 
• $16,400 or less plus $1,000 per dependent if you're claiming married filing a joint return

you qualify for No Tax Status and are not required to pay any Massachusetts income taxes.

If you don't qualify for No Tax Status, but your Massachusetts AGI doesn't exceed certain limits, you may qualify for the LIC.

Page 13 of Massachusetts' Form 1 Instructions includes a chart which shows situations in which you might claim either No Tax Status or the LIC. 

Bear in mind that you'd need to compute your Massachusetts AGI as if you're a Massachusetts resident for the entire year.  You need to include all income from whatever source derived -- Massachusetts income and non-Massachusetts source income, including any deductions from your Schedule Y, Lines 2 to 10 and Line 18 deductions. Any losses would be computed as zero.

See Learn about No Tax Status and Limited Income Credit and No Tax Status and Limited Income Credit in the Form 1 Instructions for more information."