There are A TON of limitations on your Second Amendment rights, whether or not you're under investigation.
For example:
You're not allowed to have a sound suppressor without asking the Sheriff of your County for permission, then getting fingerprinted, paying for a background check, and paying the ATF $200. Sound suppressors are MANDATORY in some European nations - as in, it's illegal to go hunting without one.
If you have a weapon with a barrel that's 16 inches long, it's perfectly legal. If you remove 1/10th of an inch of the barrel, you must also remove the stock and shoot it with one hand only, or you will go to Federal prison for ten years.
In California, it is illegal to purchase a 4th Generation Glock 19....but a 3rd Generation Glock 19 is perfectly fine (as long as you can pass the background check). The difference between a 3rd Gen and a 4th Gen is the grip, texture, and a different type of recoil spring.
Read the process required to buy a gun in New Jersey:
In summary, the process starts with your local police department. By law you must complete a form STS-33 (the application), be fingerprinted, and fill out a Consent To Mental Health Records Check from. Two references must be provided. Some police departments require that the references are not related or living with you. Please see our page on Operation Establish Compliance for information on how to deal with police departments requesting additional paperwork, interviews, and references to what the NJ State Police guidelines require.
Once the forms are complete and your references return their questionnaires, you should be issued your Firearms Purcharser's ID card within 30 days. Many citizens report that it may take up to 6 months or longer to receive your FID card depending on the police department you filed with.
After you are issued your card, you may purchase a long gun (shotgun, rifle, black powder rifle, or BB gun). If you wish to purchase a hand gun (including a BB handgun), you must apply for a Permit to Purchase a Handgun. These permits are only good for 90 days, but may be extended an additional 90 days for a total of no more than 180 at the discretion of your local police chief. You may only purchase one hand gun per month (every 30 days). Each hand gun requires its own permit. The application for a Permit to Purchase a Handgun is the same as applying for your initial Firearms ID card except finger prints are not required.
When you go to the firearms retailer, you will need to fill out the ATF from and submit to an additional background check perfromed by NJ NICS, which is NJ's version of the National Instant Background Check system. As of April 1, 2013, NJ NICS may take up to 12 days to clear you to purchase a firearm in NJ. (Nationally, these checks are returned within 20 minutes but since NJ uses it's own system, delays may take place).
Should you wish to purchase ammunition, it will be necessary to show your drivers license to purchase shotgun or rifle rounds. To purchase handgun ammunition, you will need to show your firearms ID card, or a copy of your Permit to Purchase a Handgun.
Yep. You've got to be investigated by the police before you can buy a BB gun in New Jersey.
There are a metric shitload of restrictions on the Second Amendment. Those are a few that I thought of off the top of my head, but with a little research I could go on all day.