Can New Jersey do that?

More power to them if they can, and let the other 49 take notice.

The New Jersey state Senate on Thursday overwhelmingly voted to pass a bill that would keep presidential candidates off the state’s 2020 ballot unless they release their tax returns.

According to the Courier Post, the Democratic-controlled state Senate passed the measure along party lines in a 23-11 vote on Thursday, sending the bill to the Assembly committee and full legislature for a vote before it heads to the desk of Gov. Phil Murphy (D) for consideration.

The controversial measure would deny candidates for president and vice president a spot on the state ballot if they do not publicly release five of their most recent tax returns at least 50 days before the general election in 2020.

  The Hill

If they get it on the books, I would expect a lawsuit from the RNC. But, go for it, NJ.  It ought to be an amendment to the US Constitution.  The founding fathers couldn't have foreseen the need, since there was no IRS back then.

The New Jersey legislature passed the same bill in 2017, but the measure was blocked by a veto from then-Gov. Chris Christie (R), who called it a “transparent political stunt" at the time.

Of course, but did they not have the votes to override his veto, or did they not even try? Chris Christie is a transparent political stunt.

“Today we require tax returns, but what would be next?” former California Gov. Jerry Brown (D) reportedly asked in a 2017 veto of a similar measure that was introduced in his state.

I don't know, Jerry. What? Whatever it was, it could go up for a vote, too.

“Five years of health records? A certified birth certificate? High school report cards? And will these requirements vary depending on which political party is in power?” he asked.

Not if it's federal law. And if the people think they need to know these things about their prospective president, then, yes, they should have that information. If you think your records will prevent you from being president, don't run. I draw the line at religious test. But then, so does the Constitution.

New Jersey state Sen. Joe Pennacchio (R) said in a statement to the local paper that the bill should be amended to apply to gubernatorial, state Senate and Assembly candidates, too.

Why not?

Pennacchio’s amendments have reportedly been blocked by state Democrats.

Christie was right. A transparent political stunt.

...but hey, do what you want...you will anyway.