In the letter the top official also appears to be frustrated by a lack of involvement of local officials in drawing up the policy, stating that "we would like to see a more intensive and open engagement between Whitehall and NICS (Northern Ireland Civil Service) officials".
He goes on to list seven areas in which Whitehall had not been taking full advantage of local knowledge, including on the Good Friday Agreement, North-South cooperation, and trade.
Going into detail about the issues with the UK customs proposals, Mr Sterling said plans to exempt small businesses from customs suffered from issues of practicality.
"The dividing line between businesses of different sizes in Northern Ireland supply chains will undoubtedly be blurred. This could make it difficult to accurately define which businesses are exempt from customs processes," he said.
"For example, bulk tankers owned or contracted by Irish milk processing firms collect raw milk from multiple farms in Northern Ireland before returning to Irish processing facilities."
He adds: "Small businesses trading on the island of Ireland may also be using inputs from outside these islands, or be part of an island of Ireland supply chain that ultimately sells into world markets."
The Civil Service chief also highlighted concerns with plans for a "robust enforcement mechanism" to keep goods from crossing the border.
"The visibility and impact of a 'robust enforcement mechanism' to ensure goods not complying with the EU's trade policy (whether through a lower tariff or diverging standard) stay in the UK is a significant challenge," he said.
"The example of Turkey illustrates that customs duties are only one part of the picture and technical barriers can be equally disruptive to trade.
"Potential trade barriers created by diverging tariffs or regulatory standards are therefore a key area for ongoing discussion."
In a separate leaked document also, an internal economic analysis drawn up by the Northern Ireland Executive's Department for the Economy warns that the province's economy will suffer because of Brexit, whatever solution is applied.
"There is no quick or simple solution to the land border," the assessment, dated May 2017 says.
"There is likely to be some negative impact on the economy whether border controls are sited at the land or sea border, at least in the short-to-medium term.
"The policy question is therefore how these impacts can be minimised and what transitional support is required."
The Government has declined to comment on the leaks.
There has still been little progress on the border question in talks this year, despite the opening of talks about the future relationship last week.
Under the Good Friday Agreement there can be no hard border between the Republic and Northern Ireland, and both sides agree that none should return.
The EU, however, says the customs union and single market must have external border checks to maintain their integrity.
Commission negotiators effectively proposed moving the customs checks to the Irish Sea between Britain and Northern Ireland, but Mrs May refused the approach after pressure from her allies in the DUP.
The draft withdrawal agreement as envisaged by the EU says Britain can either come up with a specific solution to the border problem, remove the need for a hard border by negotiating a close trade relationship with the EU, or revert to a "backstop" option that would keep Britain in full alignment with relevant EU regulations.
But with Mrs May having ruled out membership of the customs union and single market the chance of solving the issue using the future relationship looks slim, barring a U-turn.
Speaking in the European Parliament in Brussels on Wednesday Guy Verhofstadt, the body's Brexit coordinator, said he believed a solution the border problem was needed by the end of June.
UK Brexit Secretary David Davis said earlier this week that he was aiming for October.
Mr Verhofstadt said negotiators "still have no proposal made by the UK side that could be a satisfactory solution for the problem".