harry potter - Why didn't Dumbledore or Ministry of Magic ask for Muggle help to search for the Chamber of Secrets?

There are lots of Muggle technologies in existence which can find and map hidden structures precisely. e.g. ERT (Electrical Resistivity Tomography), BOTDR (Brillouin Optical Time Domain Reflectometry), Underground Radar, Seismic Imaging - MASW (Multichannel Analysis of Surface Waves) etc.

Talking about restriction on electricity, I believe the restriction can by lifted by the headmaster. If not, some of the techniques can work without electricity. Sometimes, all you need is ideas, not Muggle devices. e.g. vibration can be created by a wizard and a non-electric device can measure deviations in reflections. All you need is experts in the domain. Lots of hidden sections of pyramids were found even when electricity wasn't in existence.

Talking about International Statute of Wizarding Secrecy, it doesn't need to be told that Hogwarts was a wizardry school. It could easily be disguised as a Muggle castle. And, as a last line of defense, there was always memory charm.

Why didn't Dumbledore or the Ministry of Magic ask for Muggle help to search for the Chamber of Secrets?

Answer

It’s very unlikely most wizards at Hogwarts or the Ministry would consider it useful to enlist Muggle help in looking for the Chamber of Secrets, especially as it would be an inherently ‘magical’ thing, so wizards would likely be thought more capable of finding it. If skilled wizards couldn’t find it, it’s unlikely they’d think Muggles could. Hogwarts had been searched for the Chamber of Secrets by many skilled wizards and witches, who were unable to find any evidence of its existence.

“The whole thing is arrant nonsense, of course,’ he said. ‘Naturally, the school has been searched for evidence of such a chamber, many times, by the most learned witches and wizards. It does not exist. A tale told to frighten the gullible.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 9 (The Writing on the Wall)}}

It’s considered evidence against the Chamber existing that so many Hogwarts headmasters and headmistresses couldn’t find it after generations of looking for it.

“Nonsense, O’Flaherty,’ said Professor Binns in an aggravated tone. ‘If a long succession of Hogwarts headmasters and headmistresses haven’t found the thing –”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 9 (The Writing on the Wall)}}

These unsuccessful attempts to find the Chamber of Secrets had most people convinced it was a myth. After that, it’s unlikely they’d believe Muggles could find it when skilled wizards couldn’t.

“That will do,’ he said sharply. ‘It is a myth! It does not exist! There is not a shred of evidence that Slytherin ever built so much as a secret broom cupboard! I regret telling you such a foolish story! We will return, if you please, to history, to solid, believable, verifiable fact!”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 9 (The Writing on the Wall)}}

Therefore, it would likely seem silly to those in charge to call in Muggles to search for the Chamber.

Also, even if a Muggle search team was asked to search Hogwarts for the Chamber of Secrets, the majority of their equipment would likely fail, as electric devices don’t work inside Hogwarts.

“All those substitutes for magic Muggles use – electricity, and computers and radar, and all those things – they all go haywire around Hogwarts, there’s too much magic in the air.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 28 (The Madness of Mr Crouch)}}

This is because of all the magic in the air at Hogwarts, which can’t simply be removed if they want Muggles to search it. Also, radar, which would likely be one of the most useful Muggle methods of searching for the Chamber, is explicitly stated as something that won’t work in Hogwarts.