diff --git a/scan_internal.go b/scan_internal.go
index 7f7ca3274e..7ea94c4183 100644
--- a/scan_internal.go
+++ b/scan_internal.go
@@ -559,7 +559,10 @@ func (d *DB) truncateSharedFile(
 	if needsLowerTruncate {
 		sst.SmallestPointKey.UserKey = sst.SmallestPointKey.UserKey[:0]
 		sst.SmallestPointKey.Trailer = 0
-		kv := iter.SeekGE(lower, base.SeekGEFlagsNone)
+		var kv *base.InternalKV
+		if iter != nil {
+			kv = iter.SeekGE(lower, base.SeekGEFlagsNone)
+		}
 		foundPointKey := kv != nil
 		if kv != nil {
 			sst.SmallestPointKey.CopyFrom(kv.K)
@@ -598,7 +601,10 @@ func (d *DB) truncateSharedFile(
 	if needsUpperTruncate {
 		sst.LargestPointKey.UserKey = sst.LargestPointKey.UserKey[:0]
 		sst.LargestPointKey.Trailer = 0
-		kv := iter.SeekLT(upper, base.SeekLTFlagsNone)
+		var kv *base.InternalKV
+		if iter != nil {
+			kv = iter.SeekLT(upper, base.SeekLTFlagsNone)
+		}
 		foundPointKey := kv != nil
 		if kv != nil {
 			sst.LargestPointKey.CopyFrom(kv.K)
diff --git a/table_cache.go b/table_cache.go
index 3ed788961f..9a6e8a35ca 100644
--- a/table_cache.go
+++ b/table_cache.go
@@ -485,7 +485,7 @@ func (c *tableCacheShard) newIters(
 	if kinds.RangeDeletion() && file.HasPointKeys && err == nil {
 		iters.rangeDeletion, err = c.newRangeDelIter(ctx, file, cr, dbOpts)
 	}
-	if kinds.Point() && err == nil {
+	if kinds.Point() && file.HasPointKeys && err == nil {
 		iters.point, err = c.newPointIter(ctx, v, file, cr, opts, internalOpts, dbOpts)
 	}
 	if err != nil {
diff --git a/testdata/ingest_shared b/testdata/ingest_shared
index 452b20cf59..72c09b130b 100644
--- a/testdata/ingest_shared
+++ b/testdata/ingest_shared
@@ -1307,3 +1307,53 @@ next
 ----
 .
 .
+
+# Regression test for #3761. Replicate an sstable
+# which does not have point keys.
+
+reset
+----
+
+switch 2
+----
+ok
+
+batch
+range-key-set a c @4 value
+----
+
+flush
+----
+
+compact a-z
+----
+ok
+
+lsm
+----
+L6:
+  000005:[a#10,RANGEKEYSET-c#inf,RANGEKEYSET]
+
+switch 1
+----
+ok
+
+replicate 2 1 a z
+----
+replicated 1 shared SSTs
+
+lsm
+----
+L6:
+  000005(000005):[a#11,RANGEKEYSET-c#inf,RANGEKEYDEL]
+
+iter
+first
+next
+next
+next
+----
+a: (., [a-c) @4=value UPDATED)
+.
+.
+.