Justice Committee member Colin Keir has written to the Home Secretary after she threatened to end the EU-wide extraditions that have already repatriated scores of wanted men and women.
Police have voiced how deeply unhappy they are with the proposal and have been backed by Justice Secretary Kenny MacAskill, who said Ms May was "jeopardising the administration of justice in Scotland" in response to a parliamentary question from Mr Keir.
The Edinburgh Western MSP said:
"If Ms May wants to revert back to the old conventions she must explain what talks she has had on how we will deal with arrests if pulled out of the EAW.
"She must tell us if there will be guarantees in place to ensure criminals are brought to task and if other EU countries agree.
"The EWA system is not perfect and needs reformed so that only the most serious criminal cases are covered by the legislation. 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. There will be no speedy tool to extradite these criminals back to their home country to face justice.
"Why does Theresa May want to reinvent the wheel and establish bi-lateral agreements with individual member states when an effective system already exists?
"This move, as police have expressed, will have serious implications for law enforcement in Scotland and make it more difficult for to extradite criminals to Scotland. The fact is police co-operation across Europe cuts crime.
"Scotland’s interests are being actively damaged by the simmering Euro-scepticism in Westminster and yet again we are reminded of why Scotland needs its own voice in Europe as an independent country."
