The only screening they do for Kindergarten in our district is vision and hearing. Otherwise, if you're an older 4 or are 5 you can start.
They start the year slowly with writing without tears, cutting, colors, shapes, and letters. My child went in knowing these, but it doesn't mean she didn't have fun singing the songs that went with it and reading the poetry that was handed out. She thought the first 1/2 of the year was extemely easy and lots of play time for her.
Now, it's getting more difficult, because writing is not her strength. At least that's an area she can focus on.