diff --git a/clang-tools-extra/clang-tidy/performance/UnnecessaryCopyInitialization.cpp b/clang-tools-extra/clang-tidy/performance/UnnecessaryCopyInitialization.cpp
--- a/clang-tools-extra/clang-tidy/performance/UnnecessaryCopyInitialization.cpp
+++ b/clang-tools-extra/clang-tidy/performance/UnnecessaryCopyInitialization.cpp
@@ -86,7 +86,7 @@
   if (!isOnlyUsedAsConst(InitializingVar, BlockStmt, Context))
     return false;
 
-  QualType T = InitializingVar.getType();
+  QualType T = InitializingVar.getType().getCanonicalType();
   // The variable is a value type and we know it is only used as const. Safe
   // to reference it and avoid the copy.
   if (!isa<ReferenceType, PointerType>(T))
diff --git a/clang-tools-extra/test/clang-tidy/checkers/performance-unnecessary-copy-initialization.cpp b/clang-tools-extra/test/clang-tidy/checkers/performance-unnecessary-copy-initialization.cpp
--- a/clang-tools-extra/test/clang-tidy/checkers/performance-unnecessary-copy-initialization.cpp
+++ b/clang-tools-extra/test/clang-tidy/checkers/performance-unnecessary-copy-initialization.cpp
@@ -4,6 +4,7 @@
   ExpensiveToCopyType();
   virtual ~ExpensiveToCopyType();
   const ExpensiveToCopyType &reference() const;
+  const ExpensiveToCopyType *pointer() const;
   void nonConstMethod();
   bool constMethod() const;
 };
@@ -500,6 +501,25 @@
   Orig.nonConstMethod();
 }
 
+void negativeAliasNonCanonicalPointerType() {
+  ExpensiveToCopyType Orig;
+  // The use of auto here hides that the type is a pointer type. The check needs
+  // to look at the canonical type to detect the aliasing through this pointer.
+  const auto Pointer = Orig.pointer();
+  const auto NecessaryCopy = Pointer->reference();
+  Orig.nonConstMethod();
+}
+
+void negativeAliasTypedefedType() {
+  typedef const ExpensiveToCopyType &ReferenceType;
+  ExpensiveToCopyType Orig;
+  // The typedef hides the fact that this is a reference type. The check needs
+  // to look at the canonical type to detect the aliasing.
+  ReferenceType Ref = Orig.reference();
+  const auto NecessaryCopy = Ref.reference();
+  Orig.nonConstMethod();
+}
+
 void positiveCopiedFromGetterOfReferenceToConstVar() {
   ExpensiveToCopyType Orig;
   const auto &Ref = Orig.reference();