The 40-year-old woman died from her injuries following the fall at Clarendon Court, Southsea, Portsmouth, on 12 February.
A 46-year-old man, from Southsea, who was arrested on suspicion of murder, has been released with no further action to be taken, police said.
Hampshire Constabulary added it was preparing a file for the coroner.

The Somali-born author was to appear on Australian TV on Monday before starting her tour, titled "Hero of Heresy".
But she pulled out due to "a number of reasons including security concerns", event organiser Think Inc said.
Ms Hirsi Ali has faced death threats in the past.
"[She] hopes to be able to return to Australia in the not too distant future," Think Inc said in a statement.
About 2,000 tickets had been sold for the speaking events in Brisbane, Melbourne, Sydney and Auckland.
She was granted asylum in the Netherlands in 1992, and was elected as an MP in 2003.
Ms Hirsi Ali rose to international attention in 2004 as the writer of a controversial film on violence against Muslim women, Submission, after her collaborator, filmmaker Theo van Gogh, was murdered by a radical Islamist.
Having received repeated death threats over her challenges to Islam's treatment of women, Ms Hirsi Ali spent time living under 24-hour police guard.
She then moved to the United States, where she has maintained a high profile.
In an article for the Hoover Institution last month, Ms Hirsi Ali described what she called "political Islam" as being not just a religion but "a political ideology, a legal order, and in many ways also a military doctrine associated with the campaigns of the Prophet Muhammad".
Nearly 400 people had signed an online petition opposing Ms Hirsi Ali's visit to Australia and New Zealand.
"Against a backdrop of increasing global Islamophobia, Hirsi-Ali's divisive rhetoric simply serves to increase hostility and hatred towards Muslims," the petition said.
Protests had been planned at locations where she was speaking, and people who bought tickets were told their bags would be searched.
Think Inc said all ticketholders would receive refunds.

The 25-year-old joined the Shrimpers in the summer after a trial, having not played a first-team game since November 2014 while at Blackpool.
The former Newcastle and Swindon forward has since scored twice in nine Southend appearances.
Phil Brown's side are undefeated in any match Ranger has started, winning five and drawing three of the eight games.

It has been predicted more than 100,000 fans could arrive in a city with a population of less than 40,000.
"We hope the suggested figures are not the same as the actual number of fans who will turn up," Sylvain Robert told the Sport Wales TV programme.
"I don't know how we'd find space for 100,000 people."
Robert says he and the city's officials are "working on all possible scenarios" and a 10,000-capacity fan zone will be set up.
He added: "We are apprehensive about the number of fans who could arrive without a ticket as it's a problem for this type of event."
According to Paul Corkrey of the Welsh branch of the Football Supporters' Federation, Lens' Stade Bollaert-Delelis "is one of the best stadiums in France".
He added: "But the problem is that's all that's good about it.
"The fan zone is very small. To have a tournament of this size there is strange because there are not many amenities there for supporters. I wouldn't go there."
Robert is worried that the town's reputation may be damaged by the tournament.
"It's not that we would be happier to have fewer people, it's that we would be happier if we can host fans in good conditions," said the mayor.
Uefa responded with a statement, which read: "The host city of Lens, in close collaboration with the local authorities and Uefa, will be implementing appropriate measures to ensure that all visitors enjoy matches in a safe and festive atmosphere, be it at the stadium, in the fan zone or in the city centre."
Watch Sport Wales, BBC Two Wales from 19:30 BST on Friday, 6 May and later on demand and on the BBC iPlayer.
The death of a woman who fell from the window of a third-floor flat is no longer being treated as suspicious.
[NEXT_CONCEPT]
A former Dutch MP and prominent critic of conservative Islam, Ayaan Hirsi Ali, has cancelled a speaking tour of Australia and New Zealand citing security concerns.
[NEXT_CONCEPT]
Southend United striker Nile Ranger has signed a new three-and-a-half year contract with the League One club.
[NEXT_CONCEPT]
The mayor of Lens says he is apprehensive about the number of supporters expected to visit when Wales face England at Euro 2016 on 16 June.