As far as I know California has pretty strict rules on getting your car registered as soon as you move to the state or risk some hefty fines. I believe you have 30 days to get your act together.  With that said because the car is titled in your name and I'm going to go with probably insured in your name with her as a driver it's a bit of a different story and she probably has a MN license. Unless you need the car back for any type of annual inspection I would have her leave it all as is until she gets settled in. 

My first car in California came with me from New York. We had the title switched over to my name before I moved To avoid any DMV hassles. When I got to CA I was lazy and didn't do any DMV things for over a year, mostly because I was living on my friends couch and didn't have an actual address or bills in my name. When I went and got Liscense, Registration, and Smog all taken care of and brought them proof of address I did so within 30 days of establishing my own residency and avoided hefty fines.  It's an actual dollar amount per day past the 30days. I think on the form they just ask "when did you establish California residency?" Fill in as you see fit! 

To get a CA Liscense she will need the original copy of her birth certificate and social security card or a Passport and Social Security card and she'll need to take. 24 question multiple answer test. I got hung up on the having proper ID section. I thought it would be surrender my NY Liscense, get a CA Liscense but thats not the case. 

Smog, go to one of the many smog shops and ask for a test, get the form of passing and bring to the DMV.

Lastly, become a California AAA member and they'll walk you through all this without having to step into the dark-hole of an armpit that is the California DMV. If she does end up just doing everything through the DMV, save time, make an appointment and all the forms are available online! fill them out ahead of time. Go prepared with all forms for a more pleasant experience. It took me 2.5 hours to pick up custom plates for my Mini. All I had to do was hand in my old plates and get new plates, no paper work they plucked my plates out of a pile after I gave them a last name. It was so long for something so simple! 

thanks guys,   i told her at least for a year i will keep it in my name and pay the insurance,  you never know if she will want to stay.   i  told her to call the CA dmv and ask them about the rules and costs associated with a move,  that was 10 days ago,  she left a message on their system and still no call back, government at its best. 

They used to charge an "environmental impact fee" along with requiring a smog check... basically an excuse to collect a fee, even for 50 state cars, which is just about all cars in recent decades! 

If you can, I'd keep it in your name, but some areas hassle you pretty quick for an out of state car!  They really want that fee! And they might be a little annoyed that they did not collect sales tax on the original, or subsequent sale.   How can they argue with it being YOUR car you are loaning her though?

Depending on the year, she will be subject to smog inspection if she registers the car in state.

When is someone required to register an out-of-state vehicle? It's one of those things that people choose to interpret differently.

But this might help:

//dmv.ca.gov/portal/dmv/?1dmy&urile=wcm:path:/dmv_content_en/dmv/pubs/brochures/howto/htvr33

As long as you have the 50 state compliant sticker on it you should be OK its either under the hood or in the drivers door jamb

for you CA folks in the know.    one of our daughters is moving to southern CA,   she has a used mazda 3 i gave her and we checked with the dealer who says it is 50 state compliant on emissions but wont she need to have the car tested once she gets there as well?  or should i just leave the MN plates on it since it is titled in my name.