As long as you'r not using a back hoe. No. You can take a rock or two.
Only ancestors who settled in Connecticut in 1648 should have a right to any souveneirs ect.
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Let me clarify: If you have no ancestors in Connecticut in 1648 you shouldn't be taking anything.
It depends. It's illegal to remove anything from a national park (even a fallen pine cone) and many state parks have enacted similar laws. If the river is on private property and you have the owner's permission to pick up a few rocks, no problem. If not, go down to the landscaper's yard and buy a bucket full.
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Other people asked questions on various topics, and are still waiting for answer. Would be great if you can take a sec and answer them