Step 1:

Open the design you want to give a halftone dot effect.

Step 2:

Create a layer under the original design.
Create a shape that you want to convert into dots.
I copied the outside shape of my design and filled it with black.

Step 3:

You have to enlarge the shape design so far that the halftone dots are visible later created below your original.
My design is round so i can use the scaling option in Illustrator.
If your design has a special shape you have to manually adjust it.

Step 4:

Select Effect> Blur> Gaussian Blur

Use a radius you want.

The result looks like this.

Step 5:

Select Object> Rasterize ...

The resolution should be 600 dpi or more.

Step 6:

Select the object and select Effect> Pixelate> Color Halftone ...

The color halftone dialog box will open where you can enter some numbers to adjust the appearance of the effect.
Set a number for the Maximum Radius.
This will deterministically mine the size of the largest in the dot effect.
The screen angles should be equal.

Step 7:

We need to convert the raster image to vector.
Select the shape and select Object> Live Trace> Make and Expand from the menu.

The shape is now a full vector object.

Step 8:

Select with the Magic wand tool and press delete the white area.

Step 9:

Step 10:

Now we are able to assign the color and set design to the appearance of the overlay with the transparency menu.

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