diff --git a/mypy/semanal.py b/mypy/semanal.py
index d16be31e8e18..cb29377a2f9c 100644
--- a/mypy/semanal.py
+++ b/mypy/semanal.py
@@ -2931,21 +2931,34 @@ def visit_member_expr(self, expr: MemberExpr) -> None:
                 if full_name in obsolete_name_mapping:
                     self.fail("Module%s has no attribute %r (it's now called %r)" % (
                         mod_name, expr.name, obsolete_name_mapping[full_name]), expr)
-        elif isinstance(base, RefExpr) and isinstance(base.node, TypeInfo):
-            n = base.node.names.get(expr.name)
-            if n is not None and (n.kind == MODULE_REF or isinstance(n.node, TypeInfo)):
-                # This branch handles the case C.bar where C is a class and
-                # bar is a type definition or a module resulting from
-                # `import bar` inside class C. Here base.node is a TypeInfo,
-                # and again we look up the name in its namespace.
-                # This is done only when bar is a module or a type; other
-                # things (e.g. methods) are handled by other code in checkmember.
-                n = self.normalize_type_alias(n, expr)
-                if not n:
-                    return
-                expr.kind = n.kind
-                expr.fullname = n.fullname
-                expr.node = n.node
+        elif isinstance(base, RefExpr):
+            # This branch handles the case C.bar (or cls.bar or self.bar inside
+            # a classmethod/method), where C is a class and bar is a type
+            # definition or a module resulting from `import bar` (or a module
+            # assignment) inside class C. We look up bar in the class' TypeInfo
+            # namespace.  This is done only when bar is a module or a type;
+            # other things (e.g. methods) are handled by other code in
+            # checkmember.
+            type_info = None
+            if isinstance(base.node, TypeInfo):
+                # C.bar where C is a class
+                type_info = base.node
+            elif isinstance(base.node, Var) and self.type and self.function_stack:
+                # check for self.bar or cls.bar in method/classmethod
+                func_def = self.function_stack[-1]
+                if not func_def.is_static and isinstance(func_def.type, CallableType):
+                    formal_arg = func_def.type.argument_by_name(base.node.name())
+                    if formal_arg and formal_arg.pos == 0:
+                        type_info = self.type
+            if type_info:
+                n = type_info.names.get(expr.name)
+                if n is not None and (n.kind == MODULE_REF or isinstance(n.node, TypeInfo)):
+                    n = self.normalize_type_alias(n, expr)
+                    if not n:
+                        return
+                    expr.kind = n.kind
+                    expr.fullname = n.fullname
+                    expr.node = n.node
 
     def visit_op_expr(self, expr: OpExpr) -> None:
         expr.left.accept(self)
diff --git a/test-data/unit/check-modules.test b/test-data/unit/check-modules.test
index 66050601d26f..ec3eb7e9e523 100644
--- a/test-data/unit/check-modules.test
+++ b/test-data/unit/check-modules.test
@@ -1416,3 +1416,26 @@ reveal_type(f())  # E: Revealed type is 'types.ModuleType'
 reveal_type(types)  # E: Revealed type is 'types.ModuleType'
 
 [builtins fixtures/module.pyi]
+
+[case testClassImportAccessedInMethod]
+class C:
+    import m
+    def foo(self) -> None:
+        x = self.m.a
+        reveal_type(x)  # E: Revealed type is 'builtins.str'
+        # ensure we distinguish self from other variables
+        y = 'hello'
+        z = y.m.a  # E: "str" has no attribute "m"
+    @classmethod
+    def cmethod(cls) -> None:
+        y = cls.m.a
+        reveal_type(y)  # E: Revealed type is 'builtins.str'
+    @staticmethod
+    def smethod(foo: int) -> None:
+        # we aren't confused by first arg of a staticmethod
+        y = foo.m.a  # E: "int" has no attribute "m"
+
+[file m.py]
+a = 'foo'
+
+[builtins fixtures/module.pyi]
diff --git a/test-data/unit/fixtures/module.pyi b/test-data/unit/fixtures/module.pyi
index b130d795d25c..44a4dfe0c277 100644
--- a/test-data/unit/fixtures/module.pyi
+++ b/test-data/unit/fixtures/module.pyi
@@ -17,3 +17,5 @@ class tuple: pass
 class dict(Generic[T, S]): pass
 class ellipsis: pass
 
+classmethod = object()
+staticmethod = object()