The First Minister has demanded Westminster fully engages with the Scottish Government over the proposals, saying there is a “clear Scottish interest” in the plans.
In her letter to Scottish Secretary David Mundell, the SNP leader called for greater clarity over the way Bills would be assessed as applying, or not applying, to Scotland.
And she called for a meeting with Mr Mundell and Chris Grayling, the Leader of the House of Commons, to discuss the proposals.
The SNP has already called on Prime Minister David Cameron to “think again” about proposals to give English MPs a veto over legislation which affects only England, with MP Pete Wishart describing the plans as “nothing less than a constitutional outrage”.
MPs, led by Liberal Democrat Alistair Carmichael, last week staged an emergency debate on the plans, protesting that they would mean effectively an English Parliament within the ranks of the Commons - creating two tiers of MPs.
The UK Government later promised a redraft of the controversial proposals and postponed a Commons vote on the issue until at least September.
Writing to Mr Mundell today, Ms Sturgeon said the Scottish Government has “a number of concerns about the proposals”.
She wrote: “I hope that Chris’s announcement that the vote in the Commons will be delayed until September will enable further consideration including full engagement with the Scottish Government.
“There is a clear Scottish interest in Evel because of the impact it will have, and the proposals, as they currently stand, are unacceptable.”
The letter highlighted concerns about the “narrowness” of the assessment over what relates exclusively to England, with the decision limited to whether the Bill legally extends to Scotland, rather than taking into account the wider financial and policy implications.
She argued that, of the 20 Bills passed during the last parliament and listed by the UK Government as not extending to Scotland, 13 of them were actually relevant north of the border.
Of the Evel plans, Ms Sturgeon wrote: “The proposals would apply to Bills, secondary legislation and certain motions and measures (including decisions on the tuition fees cap for higher education institutions in England).
“The detail of the certification procedure for which legislation will be covered, and the Speaker’s operation of it, will be crucial.
“Proposed new standing order 83J sets out the criteria for this assessment as any clause of a Bill which relates exclusively to England or to England and Wales and is within devolved legislative competence.
“Therefore the core of these proposals involves an assessment of what is within Scotland’s devolved competence.
“This is a technical assessment where the determining factor is whether any provision of a Bill legally extends to Scotland (disregarding any minor or consequential effects).
“There is no mention of factoring into that decision any wider considerations of Bills that do not legally extend to Scotland, but could have an impact because, for example, of Barnett consequentials arising from funding changes in England and Wales associated with the policy implemented by that Bill.
“The Speaker’s assessment is limited to the legal extent, and not to the wider policy and financial implications of the Bill. This narrowness is a significant concern for me.”
The First Minister continued: “Of the 20 Bills listed by the UK Government as not extending to Scotland, no fewer than 13 of them did.
“Several of these Bills covered important areas such as charities, criminal justice and anti-slavery measures and had significant impacts on Scotland, over and above the Barnett implications that might flow from legislation.
“No doubt the UK Government will be considering the assessment when preparing your legislation but the Scottish Government has a direct interest in how the UK Government makes a judgement as to whether it considers Evel applies.”