You assume cops require a crime to have been committed before taking you....

This sounds like something you would do if you have already robbed a bank and you need to get rid of the dyed money. Buy your own dye, withdraw your own money, dye cash that you can prove is legally obtained, spend it in a bunch of places and make it a "thing", become known around town as the "crazy dyed cash dude" then start throwing your illegal cash into the mix.

Intentionally defacing/altering currency is a federal offence in itself. Though rarely enforced unless particularly egregious or you intend to defraud someone with it (like altering a 10 to be a 100 for example).

Aside from that, any business you attempted to spend it at could and likely would simply refuse to accept it.

At best you'd be left with a bunch of bills that can only really be exchanged for new ones at a bank. At worst you could face roughly $100 in fines+6mo in jail for each bill defaced.

You don't need anything special to buy those packs. The dye is made to appear black and easy to wash off, but it's actually ultraviolet pigmented and nearly impossible to wash off.

That being said, the vast majority of banks I'm familiar with just have known serial straps and/or GPS tracker straps that activate when lifted out of the drawer. Ink is a bit old-fashioned. Especially with network connected counters, it's easy enough to flag appearances of know serial bills and most robbers aren't checking the money for lumps from a GPS pack.

Also you may be missing the point of the dye a bit. It's so potent that it flags counting machines in small quantities and also cops can identify you as a suspect if it's unknowingly on your clothes, car seat, bag, etc.

I'm unsure whether people would assume you had robbed a bank, I think this would depend largely on your character / build. I know for a fact that if I did this, no one in my life would assume or think for a second that I had done that.

Would this be legal? Is there anything preventing you from dying currency, if there is no intention or act of counterfeiting?

Depends where you are but in a large number of countries it's illegal to deface currency. (This doesn't change the fact that people do deface it and I've never heard of anyone getting in trouble for it).

Shop owner's can also say no if your notes are too busted, I've had this happen before trying to purchase with bills which have a tear.

INAL but I think this could be considered destroying money. Destroying money is illegal in US so if someone would decide that dyed bills are unfit for circulation it would be a crime. I don't think there are clear laws saying that bills with dye on them are "unfit for circulation" but it sure could be argued that bills attracting attention of police are, in fact, unfit for normal use.

Is there anything legally stopping you from making your town think you're a gangster who robbed a bank and somehow got away with it?

If the goal is to convince other people to think you're a bank robber, but without actually having to rob a bank, I think it could be done with much less effort and likely more effective. But this then gets into the ethical line between little white lies and outright deception or misinformation.

Because one way to achieve that goal is to doctor a bunch of evidence that would "incriminate" yourself, such as AI-generated video, then disseminate that to local reporter s, while also plastering it on social media using astroturf accounts, and might as well stuff a copy into a manila envelope and mail to the local District Attorney.

And all of that is probably legal in most jurisdictions in the USA, with the probable sole exception of intentionally wasting the prosecutor's office's effort, since they had not solicited such evidence. Compare this to "tip lines", which expressly seek info and they are fully cognizant that not all the tips will be good.

It’s probably mostly legal. Though they might hit you with defacing currency. Technically that’s still a crime, though I don’t think it’s been used in a while.

The dye is available to the general public so that part is easy. Given how trigger happy US law enforcement is, I wouldn’t recommend doing this. Sounds like overly complicated suicide.

Ummm, so this is a weird question. It makes one think that if, one was so inclined to do so they would or have robbed a bank.