Can my Mother in Law claim my wife as a dependent because she pays for her college tuition? If so, what should I put down for the depedent status?

Does your wife live with you?  Who pays for housing, food, transportation, etc?  How old is your wife, and did she have any 2020 income (including scholarships or grants)?  Do you live in a Community Property State?

If your MIL is able to claim her under the rules, then you would have to file your own return as Married Separately.  That can be expensive taxwise. 

Q. Can my Mother in Law claim my wife as a dependent because she pays for her college tuition?

A. Simple answer: No.  But taxes aren't simple. So the real answer is maybe, but not without, essentially, your permission.

It's complicated.  For a full discussion, see https://ttlc.intuit.com/community/taxes/discussion/can-i-claim-my-daughter-who-got-married-on-december-19th-2015/00/36733?jump_to=similar-questions