Can paternity be determined by identical blood types?

If you have the same blood type, for example if both blood types are O, can that determine paternity without a DNA test?

How is paternity of a child determined by blood type analysis? Not a DNA test, but the “old fashioned” way?

Apparently, in the pre-DNA world, you could determine the paternity of a child by drawing blood from both the father and child, find their blood types, then confirm that the child could not possibly be the child of the alleged father. How is this done? Who can run this test?