Does Every state has a personal income tax. (in america)

No every state does not. There are actually 5 states that don't have taxation on residents income being Wyoming, Washington, Texas, Nevada, and South Dakota.

In one way or another, taxes are a part of every American's financial life. But for residents of Alaska, Florida, Nevada, South Dakota, Texas, Washington and Wyoming, they are off the hook for state-level personal income taxes. Additionally, two states tax dividends and investment income, but not wages