What will be the charge to file a state of Michigan tax return for 2016. I need to know before I choose to use Turbo Tax for my 2016 return for both federal and state.

There are several variables.

It first depends on whether one uses Online TurboTax or desktop (CD/download) TurboTax, and when one pays (i.e., there is a discount locked in if paid in advance in early filing season.)

Currently in Online Free Edition (Form 1040A/EZ only) the state return is free under the Absolute Zero promotion.  Later in filing season (typically sometime in March) a state return will (most likely) be 29.99 in Free Edition.  

In Online Deluxe and higher, a state return is currently discounted at 36.99.  It will be 39.99 later in filing season (typically sometime in March) if not locked in prior to the increase by paying in advance.

Most desktop products (CD/download) include a state program (Basic does NOT).  Deluxe may or may not include a state program--it comes in 2 versions--one that is Fed only, and one that is Fed and State.   If purchased from TurboTax, Deluxe includes both Fed and State.  If purchased elsewhere, one has to be careful.

With the included state program, one can prepare multiple returns of that one state.  There is a 24.99 state efile fee for each efiled state return.  There is no efile fee for New York state.  There is no fee to print and mail the state returns.

A second (additional) state program in the desktop product is currently discounted at 39.99 (normally 44.99 later in filing season.)

NOTE:
On the product pages TurboTax has a disclaimer that says for Online products: "Actual prices are determined at the time of print or e-file and are subject to change without notice. Savings and price comparisons based on anticipated price increase expected in March."

And for desktop products: "Savings and price comparison based on anticipated price increase expected in March. Prices subject to change without notice."