H.,
My daughter started doing the same thing. She would not let me brush her teeth, so I followed the steps below and it worked! The most important thing is to BE CONSISTENT with the steps and do it EVERY NIGHT:
1) Children love to imitate their parents. Talk to her and say something like, "Look, mommy is going to brush her teeth!" and turn it into something fun. Have her watch you brush your teeth while she holds her own toothbrush, and while you brush your teeth, hum a kid's song, like the Itsy Bitsy Spider.
2) Do this consistently EVERY NIGHT before she goes to bed. She may not let you brush her teeth yet, but at least she sees that this is a routine and it can be fun.
3) Once she gets interested, (she may put her toothbrush inside her mouth and this may take several days of only you brushing your teeth) have her hold her own toothbrush while you put baby toothpaste on her brush. At this age, kids like to be independent and they feel important when they do things on their own. Then brush your teeth and remember to continue humming the same song. Optimistically, this will get her interested and she’ll try to brush her teeth herself. Then, after she has “brushed” her teeth, you can take the brush from her and take over "actually" cleaning her teeth.
Good luck!
M. Penick