The US-based group said abuses had occurred in both the West Bank, where the Palestinian Authority is in power, and the Gaza Strip, run by Islamist movement Hamas.
"Both Palestinian governments, operating independently, have apparently arrived at similar methods of harassment, intimidation and physical abuse of anyone who dares criticise them," Sari Bashi, the organisation's Israel and Palestine director, said in a statement.
"The Palestinian people fought hard to gain the protections that accompany membership in the international community, and their leaders should take their treaty obligations seriously."
A spokesman for Palestinian Authority security forces in the West Bank, Adnan al-Damiri, said: "We are committed to the international treaties that we signed and respect for human rights."
He said officers were trained to avoid rights abuses.
In Gaza, interior ministry spokesman Iyad al-Bozum denied torture or political arrests. He said the Human Rights Watch report "includes many fallacies."
Human Rights Watch highlighted five cases in its report, including two in the West Bank and three in Gaza.
It said security forces arrested or questioned journalists, a political activist and two rap musicians due to "peaceful criticism of the authorities."
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According to the group, two of those arrested in Gaza and two in the West Bank said they were "physically abused or tortured".
"In the abuse cases, activists and journalists said that security officers beat or kicked them, deprived them of sleep and proper food, hosed them with cold and then hot water, and made them maintain uncomfortable positions for long hours," it said.
"In Gaza, two detainees said security officials made them sign commitments not to criticise the authorities without proper evidence. In the West Bank, both men arrested faced criminal charges, including defamation and insulting a public official."
The rights group warned that "at a time when many Palestinians are critical of their leaders, the crackdowns have a chilling effect on public debate in the traditional news media, and on social media."
Palestinian municipal elections are to be held on October 8. Hamas boycotted the last Palestinian municipal elections in 2012, but is due to participate this year.
There have been no Palestinian parliamentary elections since 2006, when Hamas won by a landslide.
In one of its examples, the Human Rights Watch report quoted a 21-year-old student in the West Bank who was a member of a rap group and who was arrested three times in 2014 and 2015.
It said the student, Mutaz Abu Lihi, was beaten and left with broken teeth at one point, while he was also harassed and pressured to work as an informant.
The report also noted that Palestinian journalists "face abuse and harassment from Israeli soldiers, who have beaten them at demonstrations, closed media offices, and arrested journalists for posing unspecified security risks."