Replace those tires now before you get stopped again, because the cop let you off easy this time and the next one might not. The 2/32 inch rule is real and most states will ticket you once you hit that mark, but here's what the other answers glossed over: some officers will cite you *before* you reach 2/32 if your tires look unsafe, especially in rain or snow conditions. It's discretionary, and if an accident happens and your tread was visibly worn, you could face liability issues way worse than a fine.
The actual penalty varies like crazy by location. Yeah, you might see fines anywhere from $100 to $500, but some states bundle it with moving violations that bump your insurance rates. A few places are lenient and hand out warnings; others treat it like a safety hazard and come down hard. The safest move is just not to gamble on this one - tires aren't that expensive compared to a ticket, increased premiums, or worse, losing control on wet pavement.
One quick check: you can use a penny. Stick it upside down into the tread grooves. If you can see Lincoln's entire head, you're at or below 2/32 and definitely need new tires. If that officer mentions it a second time, you're looking at an actual citation, not a warning.