The scooter was thrown from an over-bridge on Gartlea Road, Airdrie, North Lanarkshire, at 17:50 on Thursday, landing on top of a train.
The driver brought the train to a halt and later services on the line were subject to delays and cancellation.
BTP said the incident was "incredibly dangerous".
They appealed for anyone with information to get in touch.
PC Mark Harrigan said: "This was a particularly alarming incident for the driver of the service in question and in particular was a great inconvenience to the wider public who were subjected to lengthy delays and cancelled services as a result of this reckless act of vandalism.
"Fortunately no-one was hurt, but trespassing on the railway or risking coming into contact with overhead wires is incredibly dangerous.
"Criminal damage to the railway can result in serious and even fatal consequences for rail passengers, workers and those committing the damage."
BTP would like to speak to anyone who may have seen people acting out of the ordinary or loitering in the Gartlea Road area, adjacent to Halfords and Morrisons petrol station, around the time of the incident.

Shaw was a team-mate of Croft's in Glamorgan's County Championship winning side of 1997.
The 44-year-old will support the seconds and first team as well as the academy squad.
"As far as I'm concerned this will always be my club," Shaw said.
"There's some good young players coming through, so to build on this and help their development towards the first team is great news."
Shaw was previously appointed head coach at the county in 2007 but was subsequently replaced by Matthew Maynard.
Former captain Croft, 45, was elevated to the top role after the December departure of Toby Radford.
Shaw, who had already been working with Glamorgan's academy youngsters, joins Steve Watkin, David Harrison and Richard Almond in Croft's coaching team.

A major OECD report, published on the 28 January, ranked NI students 22nd out of 23 countries in literacy and 21st out of 23 in numeracy.
However, the OECD now say that they initially published the wrong data, and NI students are "in reality closer to mid-table of the surveyed countries".
The OECD say the mistake in the Building Skills for All report was only identified and corrected during Monday 1 February.
The new data shows that Northern Irish students rank 13 out of 23 for literacy skills, and 14 out of 23 for numeracy skills.
Northern Ireland students now rank above those in countries like the Republic of Ireland, Spain, England, the USA and Canada for reading and writing skills.
Meanwhile, Northern Ireland students rank better than those in countries like Australia, Poland, the Republic of Ireland, England and the USA for maths skills.
The OECD mistake affected rankings on the skills of university students published on pages 15 and 53 of the report.
In a statement to the BBC, an OECD spokesperson said a formatting error was to blame.
"In the course of formatting the document for publication, the graphic image for figure 3.2 (but not the title) was mistakenly replaced by the graphic image for figure 2.3," the spokesperson said.
"So while England's position changed little, Northern Ireland is, in reality, closer to mid-table of the surveyed countries."
The position of a number of other countries in the rankings was also affected and has been changed.
Finland is now the highest ranked country in the world for students literacy skills, instead of Japan.
Belgium is now the highest ranked for students' numeracy skills, instead of Finland.
The OECD say the rest of the data published in the original report is accurate.
British Transport Police (BTP) have launched an investigation after a child's scooter was thrown at a train, causing lengthy delays to services.
[NEXT_CONCEPT]
Former Glamorgan wicketkeeper Adrian Shaw has joined the Welsh county's coaching team under new head coach Robert Croft.
[NEXT_CONCEPT]
The Organisation for Economic Co-operation and Development (OECD) has apologised for publishing the wrong information about the reading, writing and maths skills of Northern Ireland university students.