diff --git a/README.md b/README.md
index de16aa6..b08ed8b 100644
--- a/README.md
+++ b/README.md
@@ -229,7 +229,8 @@ my_char_rotation = my_char_ctm.skew_x
 | Property | Description |
 |----------|-------------|
 |`page_number`| Page number on which this curve was found.|
-|`pts`| Points — as a list of `(x, top)` tuples — describing the curve.|
+|`pts`| A list of `(x, top)` tuples indicating the *points on the curve*.|
+|`path`| A list of `(cmd, *(x, top))` tuples *describing the full path description*, including (for example) control points used in Bezier curves.|
 |`height`| Height of curve's bounding box.|
 |`width`| Width of curve's bounding box.|
 |`x0`| Distance of curve's left-most point from left side of page.|
@@ -243,6 +244,7 @@ my_char_rotation = my_char_ctm.skew_x
 |`fill`| Whether the shape defined by the curve's path is filled.|
 |`stroking_color`|The color of the curve's outline. See [docs/colors.md](docs/colors.md) for details.|
 |`non_stroking_color`|The curve’s fill color. See [docs/colors.md](docs/colors.md) for details.|
+|`dash`|A `([dash_array], dash_phase)` tuple describing the curve's dash style. See [Table 4.6 of the PDF specification](https://ghostscript.com/~robin/pdf_reference17.pdf#page=218) for details.|
 |`mcid`| The [marked content](https://ghostscript.com/~robin/pdf_reference17.pdf#page=850) section ID for this curve if any (otherwise `None`). *Experimental attribute.*|
 |`tag`| The [marked content](https://ghostscript.com/~robin/pdf_reference17.pdf#page=850) section tag for this curve if any (otherwise `None`). *Experimental attribute.*|
 |`object_type`| "curve"|
diff --git a/pdfplumber/page.py b/pdfplumber/page.py
index 75437af..4a685a1 100644
--- a/pdfplumber/page.py
+++ b/pdfplumber/page.py
@@ -18,6 +18,7 @@ from pdfminer.layout import (
     LTChar,
     LTComponent,
     LTContainer,
+    LTCurve,
     LTItem,
     LTPage,
     LTTextContainer,
@@ -59,10 +60,9 @@ ALL_ATTRS = set(
         "evenodd",
         "fill",
         "non_stroking_color",
-        "path",
-        "stream",
         "stroke",
         "stroking_color",
+        "stream",
         "mcid",
         "tag",
     ]
@@ -383,9 +383,15 @@ class Page(Container):
             if isinstance(attr["fontname"], bytes):
                 attr["fontname"] = fix_fontname_bytes(attr["fontname"])
 
-        if "pts" in attr:
+        elif isinstance(obj, (LTCurve,)):
             attr["pts"] = list(map(self.point2coord, attr["pts"]))
 
+            # Ignoring typing because type signature for obj.original_path
+            # appears to be incorrect
+            attr["path"] = [(cmd, *map(self.point2coord, pts)) for cmd, *pts in obj.original_path]  # type: ignore  # noqa: E501
+
+            attr["dash"] = obj.dashing_style
+
         if "y0" in attr:
             attr["top"] = self.height - attr["y1"]
             attr["bottom"] = self.height - attr["y0"]
diff --git a/tests/test_convert.py b/tests/test_convert.py
index fd488c5..78731bf 100644
--- a/tests/test_convert.py
+++ b/tests/test_convert.py
@@ -177,8 +177,8 @@ class Test(unittest.TestCase):
         c = self.pdf.to_csv(precision=3)
         assert c.split("\r\n")[9] == (
             "char,1,45.83,58.826,656.82,674.82,117.18,117.18,135.18,12.996,"
-            '18.0,12.996,,,,,,TimesNewRomanPSMT,,,"(1, 0, 0, 1, 45.83, 660.69)"'
-            ',,DeviceRGB,"(0, 0, 0)",,,18.0,,,,,,,Y,,1,'
+            '18.0,12.996,,,,,,,TimesNewRomanPSMT,,,"(1, 0, 0, 1, 45.83, 660.69)"'
+            ',,DeviceRGB,"(0, 0, 0)",,,,18.0,,,,,,,Y,,1,'
         )
 
         io = StringIO()
@@ -244,8 +244,8 @@ class Test(unittest.TestCase):
 
         assert res.decode("utf-8").split("\r\n")[9] == (
             "char,1,45.83,58.826,656.82,674.82,117.18,117.18,135.18,12.996,"
-            '18.0,12.996,,,,,,TimesNewRomanPSMT,,,"(1, 0, 0, 1, 45.83, 660.69)"'
-            ',,DeviceRGB,"(0, 0, 0)",,,18.0,,,,,,,Y,,1,'
+            '18.0,12.996,,,,,,,TimesNewRomanPSMT,,,"(1, 0, 0, 1, 45.83, 660.69)"'
+            ',,DeviceRGB,"(0, 0, 0)",,,,18.0,,,,,,,Y,,1,'
         )
 
     def test_cli_csv_exclude(self):
@@ -270,8 +270,8 @@ class Test(unittest.TestCase):
 
         assert res.decode("utf-8").split("\r\n")[9] == (
             "char,1,45.83,58.826,656.82,674.82,117.18,117.18,135.18,12.996,"
-            "18.0,12.996,,,,,,TimesNewRomanPSMT,"
-            ',,"(0, 0, 0)",,18.0,,,,,,Y,,1,'
+            "18.0,12.996,,,,,,,TimesNewRomanPSMT,"
+            ',,"(0, 0, 0)",,,18.0,,,,,,Y,,1,'
         )
 
     def test_cli_csv_include(self):