diff --git a/httpcore/_backends/curio.py b/httpcore/_backends/curio.py
index c959ddbb..ef9a11c1 100644
--- a/httpcore/_backends/curio.py
+++ b/httpcore/_backends/curio.py
@@ -1,5 +1,7 @@
-from ssl import SSLContext
-from typing import Optional
+import select
+import socket
+from ssl import SSLContext, SSLSocket
+from typing import Dict, Optional, Type, Union
 
 import curio
 import curio.io
@@ -10,6 +12,7 @@
     ConnectTimeout,
     ReadError,
     ReadTimeout,
+    TimeoutException,
     WriteError,
     WriteTimeout,
     map_exceptions,
@@ -50,7 +53,13 @@ def semaphore(self) -> curio.Semaphore:
         return self._semaphore
 
     async def acquire(self, timeout: float = None) -> None:
-        await self.semaphore.acquire()
+        exc_map: Dict[Type[Exception], Type[Exception]] = {
+            curio.TaskTimeout: TimeoutException,
+        }
+        acquire_timeout: int = convert_timeout(timeout)
+
+        with map_exceptions(exc_map):
+            return await curio.timeout_after(acquire_timeout, self.semaphore.acquire())
 
     async def release(self) -> None:
         await self.semaphore.release()
@@ -64,10 +73,14 @@ def __init__(self, socket: curio.io.Socket) -> None:
         self.stream = socket.as_stream()
 
     def get_http_version(self) -> str:
-        if hasattr(self.socket, "_socket") and hasattr(self.socket._socket, "_sslobj"):
-            ident = self.socket._socket._sslobj.selected_alpn_protocol()
-        else:
-            ident = "http/1.1"
+        ident: Optional[str] = "http/1.1"
+
+        if hasattr(self.socket, "_socket"):
+            raw_socket: Union[SSLSocket, socket.socket] = self.socket._socket
+
+            if isinstance(raw_socket, SSLSocket):
+                ident = raw_socket.selected_alpn_protocol()
+
         return "HTTP/2" if ident == "h2" else "HTTP/1.1"
 
     async def start_tls(
@@ -118,11 +131,13 @@ async def write(self, data: bytes, timeout: TimeoutDict) -> None:
                 await curio.timeout_after(write_timeout, self.stream.write(data))
 
     async def aclose(self) -> None:
-        # we dont need to close the self.socket, since it's closed by stream closing
         await self.stream.close()
+        await self.socket.close()
 
     def is_connection_dropped(self) -> bool:
-        return self.socket._closed
+        rready, _, _ = select.select([self.socket.fileno()], [], [], 0)
+
+        return bool(rready)
 
 
 class CurioBackend(AsyncBackend):
diff --git a/tests/marks/curio.py b/tests/marks/curio.py
index 7504ee8f..616b2766 100644
--- a/tests/marks/curio.py
+++ b/tests/marks/curio.py
@@ -19,7 +19,7 @@ def curio_pytest_pycollect_makeitem(collector, name, obj):
     if collector.funcnamefilter(name) and _is_coroutine(obj):
         item = pytest.Function.from_parent(collector, name=name)
         if "curio" in item.keywords:
-            return list(collector._genfunctions(name, obj))
+            return list(collector._genfunctions(name, obj))  # pragma: nocover
 
 
 @pytest.hookimpl(tryfirst=True, hookwrapper=True)