The CDC says the TLV for chlorine is 1.5 mg/m3. Note, that this is per cubic meter and
not per liter. So a TLV of 0,0015 mg/l vs 4 mg/l in US drinking water.
Here is the source, as you requested:
https://www.cdc.gov/niosh/idlh/7782505.html
And here the definition of TLV from Wikipedia:
The threshold limit value (TLV) is a level of occupational exposure to a hazardous substance where it is believed that nearly all healthy workers can repeatedly experience at or below this level of exposure without adverse effects.
So much for that, but it is only half the story. Chlorine is a gas and therefore volatile. The measured chlorine in the waterworks says little about the amount that ends up in your body.
What it does though is, that it forms compounds with organic substances (the microorganisms it kills) in the water, which in turn can be toxic or carcinogenic.
Instead of regulating the volatile chlorine it makes much more sense to regulate the harmful compounds, which is exactly what many European countries do.