Judge Judy says there could be real danger in letting Lindsay Clancy's murder case end with a hung jury ... and she thinks Lindsay should be back before a judge.

We got the famous TV judge out in NYC and asked what she made of Clancy's mistrial and whether she thinks the Massachusetts mom is guilty of murder.

Judy had a pretty simple take ... there's no question Clancy killed her three children, but whether there's an excuse for it is another matter.

We then asked if Clancy should be retried ... and Judy made clear she sees a real danger in not putting her back on trial.

Of course, the case ended in a mistrial earlier this month ... after jurors couldn't agree on whether Clancy should be held criminally responsible.

We also asked Judy about Nancy Mace's comments to TMZ DC earlier this week ... when the congresswoman said Clancy should be publicly executed.

Judy's response was short and sharp ... and let's just say she's not on Mace's wavelength.

So, Judy clearly isn't giving Clancy a pass ... but she's also not signing off on every punishment being floated.