My mother in law got her green card this year and she has been going back and forth between the US and europe ever since. She lives with us when ever she is in the US. Can I claim her as and dependent? =========>>>>yes you can claim your MIL as your dependent as a qualifying relative aslongas her gross income for the year of 2015 must be less than $4K, $3,950 for 2014 and you must generally provide more than half of her total support during the year of 2015.She does not need to live with you for more than half of the year 2015.
Or she has to file her own taxes?=======>It depends; as a dependent,her standard deduction is generally limited to the larger of:
Unearned income of $1K(interest, dividend or capital gain), or her earned income plus $350, but not more than the regular standard deduction (generally $6.3K for 2015 plus her additional deduction of $1550 if she is older than 65 years old and single ).for example, If she is 65 or older and her unearned income exceeds $2.25K, then yes she needs to file return even if there is no tax liability .