Karen Mathews, 51, snapped after facing a two-year campaign of harassment and told police she would kill Vicki Blair, 61.
Perth Sheriff Court was told Ms Blair had subjected Mrs Mathews and her husband Keith to "two years of hell" despite an interdict granted against the pensioner.
And the court heard their local MSP, Scotland's finance secretary John Swinney, was forced to step in when the council dropped plans to make Ms Blair subject to an anti-social behaviour order.
Perth and Kinross Council's community safety team were working on an ASBO but dropped the idea when Ms Blair was diagnosed as having a mental disorder.
It was when they sent a letter to Mrs and Mrs Mathews informing them they could take no further steps under national guidelines that Mrs Mathews - who has no previous convictions - snapped.
She had an argument with her husband and called the police herself. She then told the officers: "I shouldn't tell you this, but I'm going to kill her. I can't take any more of this."
When the officers warned her, she continued: "OK, what if I don't kill her and I just knock her out. What's wrong with that? Next time she's out the front I'm going to do that."
Fiscal depute Stuart Richardson told the court that Mrs Mathews was arrested and held at the local police station. Yesterday she admitted making threats to kill Vicki Blair at McLaren Court, Blairgowrie, on 14 March.
Solicitor Mike Tavendale, defending, said: "Mrs Blair has been trying to goad Mr and Mrs Mathews. When Mrs Mathews exits the house she will come out with a hand-held video camera and follow her every move.
"When she gets in the car Mrs Blair comes right up with the video camera.
"It's that sort of behaviour. This is the culmination of two years of hell they have gone through at the hands of their neighbour."
Mr Tavendale said Mrs Mathews had no record whatsoever.
He added: "A year and a half ago an interim interdict was raised. Over 18 months the Safer Community Scheme have been provided with voluminous information and appeared on the point of raising ASBO proceedings."
He told the court Mrs and Mrs Mathews had tried to sell their home to escape from Mrs Blair and would move out later this month.
He said: "Somewhat ironically, I received a letter from John Swinney to say that after pressure, not just from the Mathews, but other neighbours, Perth and Kinross Council have now reopened the case to consider matters afresh."
The Mathews had reported Mrs Blair for a sustained course of bizarre behaviour including using her garden hose over the fence to dowse their barbecue.
She reportedly set up a bird feeder in a spot which led to flocks of birds making a mess of the Mathews vehicles which were parked nearby.
They also accused her of gardening noisily after midnight and repeatedly setting off car alarms.
Mrs Blair was previously convicted of breaching the peace by raising her middle finger to Mr Mathews even though she claimed she did it because of a medical condition.
Mrs Blair was found guilty of breaching the peace on 19 May last year by making an offensive gesture at Keith Matthews. She was fined £350.
Mr Matthews said that living next door to the American was like "Chinese water torture" and her bizarre behaviour had caused him and his wife Karen enormous stress.
Yesterday, Sheriff Lindsay Foulis told Mrs Mathews he would order her to behave for three months and if she kept out of trouble he would admonish her.