Can I apply for Medicaid just for my wife separately?

Yes, she applies separately. Joint assets are included, usually the house and possibly some bank accounts.

For couples Medicaid gets complex as your overall joint income & assets are looked at for medicaid eligibility for your wife BUT you as the "community spouse" are not required to become impoverished as only your "at need" spouse needs to meet medicaid medical "at need" health history & financial limits (Usuaaly 2k non exempt assets and under $2,100 income). Personally I think a son or daughter who was involved in their widow/widower parents life can do & deal with the Medicaid application even if the parent owns their home & has a car. But for a CS, you need an elder law atty and need to see one BeFORE ever applying for medicaid. I'd go with one who is NAELA certified as CS stuff is just gonna be complex.

For CS situations, in general they are allowed about 117k in non exempt assets plus a home & 1car (both within certain assessor value). Whole life policies with cash value, 401ks, investments, property other than homestead property, savings etc could take you over the 117k allowed. Sometimes there are things that can be done in advance of the medicaid application to have nonexempt assets become exempt and within Medicaid compliance. That's what a good NAELA atty can do as they know what works for just how your states laws & Medicaid program run. Not a DIY project. Really truly get an atty.

For CS, it seems state's set a "snapshot" day at which the couples assets & income are fixed at. Usually the date of the application. So whatever sale, transfer, etc need to be done & through your bank account before ever dealing with Medicaid.

There are things you don't think about that can become an issue too.....like most couples have each other as beneficiary to insurance. If you should predecease her, she will get the $ from the life insurance policy and it will take her over medicaid limits and she becomes ineligible. So who will be there for her to deal with all this? Your dead, so who? It's little things like this, that your atty will have foreseen for you both. Btw I'm not an atty.