The NLD, which has publicly called on people to vote "no", said it had reported the incidents but the authorities had not investigated.
"The responsible authorities have never done any investigating, charging or taking any action to uphold law and order over those crimes committed against NLD party members," the party said.
The party accused the government of intimidation, saying six NLD members have been attacked since the announcement in February that a referendum on the proposed constitution would be held.
One member needed 21 stitches to his head after an assault, which also affected his vision.
The party said another 20 of its members, wearing T-shirts printed with the word "no", were arrested in the western port of Sittwe and tortured while detained for investigation.
Officials have not commented on the party's charges, but the government has said the vote will be held in a "systematic and fair manner", state media reported on Saturday.
Vice-Senior General Maung Aye, the military government's second in command, told a passing out parade for army recruits that the military was trying to produce a constitution that would pave the way to democracy, the New Light of Myanmar newspaper reported.
"Some dissidents at home and abroad are making attempts to undermine the process of the systematic handover of the state power"
Myanmar vice senior-general
"Comrades, it is the Tatmadaw [military] that is constantly striving for the emergence of a constitution capable of shaping the multiparty democracy system," the general said.
"The Commission for Holding Referendum will organise the national referendum in a systematic and fair manner for approving of the draft constitution on 10 May," he said.
Maung Aye also appeared to give a warning to opponents of the charter.
"Some dissidents at home and abroad are making attempts to undermine the process of the systematic handover of the state power by the Tatmadaw," he said.
"However, I would like to assert that the Tatmadaw will put in the fore the wishes of the people."
State media have been giving extensive coverage to government slogans and activities promoting a "yes" vote as a patriotic duty and have not reported any opposition to the proposed constitution.
"To approve the state constitution is a national duty of the entire people today. Let us all cast 'yes' vote in the national interest," the New Light of Myanmar said in a front-page banner on Saturday.
Meanwhile, in Japan on Saturday, Myanmar demonstrators scuffled with Japanese police outside the Myanmar embassy in Tokyo.
Ten demonstrators were injured and Yoshinori Nagashiki, a Tokyo fire department spokesman, said eight of them had been taken to a hospital for treatment, though details of their injuries are not immediately known.
About 150 Myanmar residents in Japan are demanding they be allowed to vote on the draft charter ahead of the referendum over the constitution.
The May 10 ballot will be the first in Myanmar since 1990, when Aung San Suu Kyi, the NLD leader, won a landslide victory that has never been recognised by Myanmar's military rulers.