The Home Secretary sparked concern among Scottish law enforcement officials when she said the UK was "minded" to retreat from crime-fighting agreements finalised under the Lisbon Treaty.
Senior police officers north of the Border fear her move, thought to be designed to assuage her party's Eurosceptic minority, could make it harder to extradite British criminals from Europe.
Scottish Justice Secretary Kenny MacAskill has accused Ms May of "jeopardising the administration of justice in Scotland". Now SNP backbencher Colin Keir wants to know how the UK's European partners are reacting to the proposed move.
He said: "Theresa May must tell us what discussions she has had with other EU countries on the consequences of dealing with crime if the UK Government opts out of European arrest warrants.
"She must tell us if there will be guarantees in place to ensure criminals are brought to task and if other EU countries agree.
"Instead of pulling out of Europe's only tool to fight cross-border crime they should be working with our neighbours to improve it.
"There is a real danger that by pulling out Theresa May will create a safe-haven for European criminals."