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What is the Tolerance on a Centerline?

I know its a goofy question. Basically I inherited a bunch of tooling prints where the engineer (now me) is trying to convey that features need to be in the center of the part. They give the overall dimensions with a relatively loose tolerance and then draw a centerline and dimension any additional features off the centerline. They do this because the overall dimensions of the part are not that important, but what is important is that the features are centered in the part. On this example part how far out of center could the hole be while still being to print? And is there a better way of dimensioning this? Also, the people making these parts do not have the ability to use a CMM. Thank you very much guys.