Many public schools will post their early entrance or grade skipping policy on their websites somewhere. Look for a district policy link. Many districts won't publicize this too heavily but policies probably exist.

For example, ours won't admit early K (ie must be 5 yo), will only do early 1st if they are coming from another state but in 2nd grade you can enter them in whichever grade is appropriate. There is also a policy set out to skip grades and/or accelerate in a subject (for MS and HS).